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Surface Area of Prisms and Cylinders
Retrieved from http://www.mrhammond.org/math/mathlessons/
Vocabulary• A net is a pattern you can fold to
form a three-dimensional figure.
This is a net for a triangular prism.
• The surface area of a three-dimensional figure is the sum of the areas of its surfaces.
• Find the area of each surface, and add all the areas together.
Example 1
26 cm
8 cm18 cm
Triangles
A = ½ bhA = ½ (26)(18)A = ½ (468)A = 234 cm2
2 Tri’s: 234 x 2 = 468 cm2
Left Rectangle
A = lwA = (18)(8)A = 144 cm2
Front and Back RectanglesA = lwA = (26)(8)A = 208 cm2
2 Rect’s: 208 x 2 = 416 cm2
Add up the areas to find surface area.
S.A. = 468 cm2 + 144 cm2 + 416 cm2
S.A. = 1,028 cm2
Surface Area of a Cube
• A cube has 6 congruent square faces.
• Find the area of one face, and multiply it by 6.
Example
7 in
A = s2
A = 72
A = 49 in2
S.A. = 49(6)
S.A. = 294 in2
Surface Area of a Rectangular Prism
• The surface area of a rectangular prism is the area of the six rectangles that cover it.
• To find the surface area, we don't have to figure out all six because we know that the top and bottom (length x width) are the same, the front and back (length x height) are the same, and the left and right sides (width x height) are the same.
• So, we can use the formula SA = 2(lh) + 2(lw) + 2(wh)
Surface Area of a Rectangular Prism
10 cm
7 cm
6 cm
SA = 2(lh) + 2(lw) + 2(wh)
SA = 2(6cm x 10cm) + 2(6cm x 7cm) + 2(7cm x 10cm)
SA = 2(60cm²) + 2(42cm²) + (70cm²)
SA = 120cm² + 84cm² + 140cm²
SA = 344cm²
Surface Area of a Cylinder• A cylinder consists of two circle bases
and one rectangular side.
• The length of the rectangle is equal to the circumference of the circle.
• Find the area of the circles and add it to the area of the rectangle.
Example5 m
16 m
Area of the circles
A = r2
A = 3.14(52)A = 3.14 (25)A = 78.5 m2
2 circles: 78.5 x 2 = 157 m2
Rectangle
The width of the rectangle is the height of the cylinder (16 m). The length of the rectangle is the circumference of the circle.
C = 2rC = 2(3.14)(5)C = 31.4 m
A = lwA = 31.4(16)A = 502.4 m2
Put the areas together:
S.A. = 157 m2 + 502.4 m2
S.A. = 659.4 m2
Homework Time
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