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Surface Area of 3 – Dimensional Figures. Cubes and Rectangular Prisms. Definition. Surface area is the sum of the areas of all the surfaces of a 3 – Dimensional figure. It is basically the outside layer or surface. Example: When you paint a wall, you are painting the surface of the wall. - PowerPoint PPT Presentation
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Surface Area of Surface Area of 3 ndash Dimensional 3 ndash Dimensional
FiguresFigures
Cubes and Rectangular Cubes and Rectangular PrismsPrisms
DefinitionDefinition Surface area is the sum of the areas of all Surface area is the sum of the areas of all
the surfaces of a 3 ndash Dimensional figurethe surfaces of a 3 ndash Dimensional figure It is basically the outside layer or surfaceIt is basically the outside layer or surface Example When you paint a wall you are Example When you paint a wall you are
painting the surface of the wallpainting the surface of the wall
Surface Area of CubesSurface Area of Cubes Remember that a cube is made up of Remember that a cube is made up of
squares on all sides There are 6 sides to squares on all sides There are 6 sides to a cube just like dice Therefore there are a cube just like dice Therefore there are 6 squares total To find the surface area 6 squares total To find the surface area find the area of one square and then find the area of one square and then multiply by 6 Simply use the following multiply by 6 Simply use the following formula formula
SA = 6sSA = 6s22
ExampleExample
Find the surface area of the cubeFind the surface area of the cube Recall that all of the sides of a square are Recall that all of the sides of a square are
the same length So all you have to do is the same length So all you have to do is multiply the sidesmultiply the sides
Find the area first The length and the width Find the area first The length and the width are both 4 cm 4 x 4 = 16 Thus the area of are both 4 cm 4 x 4 = 16 Thus the area of one square is 16 cmone square is 16 cm22 Now multiply by 6 Now multiply by 6 and we see that the surface area is 96 cmand we see that the surface area is 96 cm22
4 cm
4 cm
YOUR TURNYOUR TURN
Find the surface area of the following cubeFind the surface area of the following cube What is the length and width of the cube 7 mmWhat is the length and width of the cube 7 mm Now find the area of one square 7 x 7 = 49 Now find the area of one square 7 x 7 = 49
Thus the area of one square is 49 mmThus the area of one square is 49 mm22 Take this and multiply by 6 and 49 x 6 = Take this and multiply by 6 and 49 x 6 = 294 mm294 mm22 So the surface area of the cube is 294 mmSo the surface area of the cube is 294 mm22
7 mm
7 mm
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
DefinitionDefinition Surface area is the sum of the areas of all Surface area is the sum of the areas of all
the surfaces of a 3 ndash Dimensional figurethe surfaces of a 3 ndash Dimensional figure It is basically the outside layer or surfaceIt is basically the outside layer or surface Example When you paint a wall you are Example When you paint a wall you are
painting the surface of the wallpainting the surface of the wall
Surface Area of CubesSurface Area of Cubes Remember that a cube is made up of Remember that a cube is made up of
squares on all sides There are 6 sides to squares on all sides There are 6 sides to a cube just like dice Therefore there are a cube just like dice Therefore there are 6 squares total To find the surface area 6 squares total To find the surface area find the area of one square and then find the area of one square and then multiply by 6 Simply use the following multiply by 6 Simply use the following formula formula
SA = 6sSA = 6s22
ExampleExample
Find the surface area of the cubeFind the surface area of the cube Recall that all of the sides of a square are Recall that all of the sides of a square are
the same length So all you have to do is the same length So all you have to do is multiply the sidesmultiply the sides
Find the area first The length and the width Find the area first The length and the width are both 4 cm 4 x 4 = 16 Thus the area of are both 4 cm 4 x 4 = 16 Thus the area of one square is 16 cmone square is 16 cm22 Now multiply by 6 Now multiply by 6 and we see that the surface area is 96 cmand we see that the surface area is 96 cm22
4 cm
4 cm
YOUR TURNYOUR TURN
Find the surface area of the following cubeFind the surface area of the following cube What is the length and width of the cube 7 mmWhat is the length and width of the cube 7 mm Now find the area of one square 7 x 7 = 49 Now find the area of one square 7 x 7 = 49
Thus the area of one square is 49 mmThus the area of one square is 49 mm22 Take this and multiply by 6 and 49 x 6 = Take this and multiply by 6 and 49 x 6 = 294 mm294 mm22 So the surface area of the cube is 294 mmSo the surface area of the cube is 294 mm22
7 mm
7 mm
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
Surface Area of CubesSurface Area of Cubes Remember that a cube is made up of Remember that a cube is made up of
squares on all sides There are 6 sides to squares on all sides There are 6 sides to a cube just like dice Therefore there are a cube just like dice Therefore there are 6 squares total To find the surface area 6 squares total To find the surface area find the area of one square and then find the area of one square and then multiply by 6 Simply use the following multiply by 6 Simply use the following formula formula
SA = 6sSA = 6s22
ExampleExample
Find the surface area of the cubeFind the surface area of the cube Recall that all of the sides of a square are Recall that all of the sides of a square are
the same length So all you have to do is the same length So all you have to do is multiply the sidesmultiply the sides
Find the area first The length and the width Find the area first The length and the width are both 4 cm 4 x 4 = 16 Thus the area of are both 4 cm 4 x 4 = 16 Thus the area of one square is 16 cmone square is 16 cm22 Now multiply by 6 Now multiply by 6 and we see that the surface area is 96 cmand we see that the surface area is 96 cm22
4 cm
4 cm
YOUR TURNYOUR TURN
Find the surface area of the following cubeFind the surface area of the following cube What is the length and width of the cube 7 mmWhat is the length and width of the cube 7 mm Now find the area of one square 7 x 7 = 49 Now find the area of one square 7 x 7 = 49
Thus the area of one square is 49 mmThus the area of one square is 49 mm22 Take this and multiply by 6 and 49 x 6 = Take this and multiply by 6 and 49 x 6 = 294 mm294 mm22 So the surface area of the cube is 294 mmSo the surface area of the cube is 294 mm22
7 mm
7 mm
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
ExampleExample
Find the surface area of the cubeFind the surface area of the cube Recall that all of the sides of a square are Recall that all of the sides of a square are
the same length So all you have to do is the same length So all you have to do is multiply the sidesmultiply the sides
Find the area first The length and the width Find the area first The length and the width are both 4 cm 4 x 4 = 16 Thus the area of are both 4 cm 4 x 4 = 16 Thus the area of one square is 16 cmone square is 16 cm22 Now multiply by 6 Now multiply by 6 and we see that the surface area is 96 cmand we see that the surface area is 96 cm22
4 cm
4 cm
YOUR TURNYOUR TURN
Find the surface area of the following cubeFind the surface area of the following cube What is the length and width of the cube 7 mmWhat is the length and width of the cube 7 mm Now find the area of one square 7 x 7 = 49 Now find the area of one square 7 x 7 = 49
Thus the area of one square is 49 mmThus the area of one square is 49 mm22 Take this and multiply by 6 and 49 x 6 = Take this and multiply by 6 and 49 x 6 = 294 mm294 mm22 So the surface area of the cube is 294 mmSo the surface area of the cube is 294 mm22
7 mm
7 mm
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
YOUR TURNYOUR TURN
Find the surface area of the following cubeFind the surface area of the following cube What is the length and width of the cube 7 mmWhat is the length and width of the cube 7 mm Now find the area of one square 7 x 7 = 49 Now find the area of one square 7 x 7 = 49
Thus the area of one square is 49 mmThus the area of one square is 49 mm22 Take this and multiply by 6 and 49 x 6 = Take this and multiply by 6 and 49 x 6 = 294 mm294 mm22 So the surface area of the cube is 294 mmSo the surface area of the cube is 294 mm22
7 mm
7 mm
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
Rectangular PrismsRectangular Prisms To find the surface area of a prism you have to To find the surface area of a prism you have to
find the areas of all the sides and add them upfind the areas of all the sides and add them up Understand that there are still 6 sides to a prism Understand that there are still 6 sides to a prism
and that opposite sides are the same shapeand that opposite sides are the same shape To find the surface area of a rectangular prism To find the surface area of a rectangular prism
use the following formulause the following formula SA = 2(wh + lh + lw)SA = 2(wh + lh + lw)
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
ExampleExample Find the surface area of the prismFind the surface area of the prism
12 m
7 m1 m
SA = 2(1 x 7 + 12 x 7 + 12 x 1)SA = 2 (7 + 84 + 12)SA = 2 (103)SA = 206The surface area is 206 m2 Surface area is just like finding the regular area The unit of measurement is squared
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
TAKE THE CHALLENGETAKE THE CHALLENGE
You find the surface area of the following You find the surface area of the following prismprism
4 ft26 ft
7 ft
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
CHALLENGE ContCHALLENGE Cont SA = 2(4 x 7 + 26 x 7 + 26 x 4)SA = 2(4 x 7 + 26 x 7 + 26 x 4) SA = 2(28 + 182 + 104)SA = 2(28 + 182 + 104) SA = 2(314)SA = 2(314) SA = 628SA = 628 The surface area is 628 ftThe surface area is 628 ft22
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
SAMPLE ARMT QUESTIONSAMPLE ARMT QUESTION David has two shapes he is painting for a David has two shapes he is painting for a
project For each of the two shapes he will project For each of the two shapes he will paint only the outside including the lidpaint only the outside including the lid
One shape is a cylindrical can with a radius of 4 One shape is a cylindrical can with a radius of 4 inches and a height of 9 inchesinches and a height of 9 inches
The other shape is a rectangular prism-shaped The other shape is a rectangular prism-shaped box The box is 3 inches wide 8 inches long box The box is 3 inches wide 8 inches long and 5 inches highand 5 inches high
Which shape has the greater surface area for Which shape has the greater surface area for David to paintDavid to paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
Sample ARMT Question ContSample ARMT Question Cont First find the surface area of the cylinderFirst find the surface area of the cylinder Formula (2 x 314 x r x h) + (2 x 314 x rFormula (2 x 314 x r x h) + (2 x 314 x r22)) Stick the numbers in directlyStick the numbers in directly (2 x 314 x 4 x 9) + (2 x 314 x 4 x 4)(2 x 314 x 4 x 9) + (2 x 314 x 4 x 4) This equals 22608 + 10048This equals 22608 + 10048 Add these together and the surface area of the Add these together and the surface area of the
cylinder is 32656 square inchescylinder is 32656 square inches
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
Sample ARMT Question ContSample ARMT Question Cont Next find the surface area of the rectangular Next find the surface area of the rectangular
prismprism Formula 2(wh + lh + lw)Formula 2(wh + lh + lw) Stick the numbers in directlyStick the numbers in directly 2(32(35 + 85 + 85 + 85 + 83)3) This equals 2(15 + 40 + 24)This equals 2(15 + 40 + 24) This equals 2(79) = 158This equals 2(79) = 158 The surface area of the rectangular prism is 158 The surface area of the rectangular prism is 158
square inchessquare inches
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
ANSWERANSWER
The cylinder has a surface area of 32656 The cylinder has a surface area of 32656 square inchessquare inches
The rectangular prism has a surface area of The rectangular prism has a surface area of 158 square inches 158 square inches
The cylindrical can has the greater surface area The cylindrical can has the greater surface area to paintto paint
