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Surface Area
Surface AreaPrisms and Cylinder
by Maria Gloria G. GabunadaBSEd – Math 42011 – 2012
What is a SURFACE
AREA?
What is a SURFACE AREA?
What is a SURFACE AREA?
Is the sum of the areas of all the faces of a solid.
What is a SURFACE AREA?
What is a SURFACE AREA?
The unit for surface area is expressed in
square units.
SURFACE AREA of a
Rectangular Prism
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
Recall:
• A rectangular prism is a solid (3-dimensional) object which has six faces that are rectangles.
• Area of a rectangular prism is given by the formula:– A = LW
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
A1 = LW
Length (L)
Wid
th (W
)Height (H)
A3 = LW
A2 = L H
A4 = L H
A 4 = W
H
A 5 =
WH
H
W
L
W
To get the surface area of a rectangular prism (SAr):
SAr = A1 + A2 + A3 + A4 + A5 + A6
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
A1 = LW
Length (L)
Wid
th (W
)Height (H)
A3 = LW
A2 = L H
A4 = L H
A 4 = W
H
A 5 =
WH
H
W
L
W
To get the surface area of a rectangular prism (SAr):
SAr = A1 + A2 + A3 + A4 + A5 + A6
Note: A1 = A3 ; A2 = A4 ; A5 = A6
SAr = 2A1 + 2A2 + 2A5
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
A1 = LW
Length (L)
Wid
th (W
)Height (H)
A3 = LW
A2 = L H
A4 = L H
A 4 = W
H
A 5 =
WH
H
W
L
W
To get the surface area of a rectangular prism (SAr):
SAr = A1 + A2 + A3 + A4 + A5 + A6
Note: A1 = A3 ; A2 = A4 ; A5 = A6
SAr = 2A1 + 2A2 + 2A5
By substitution, we get
SAr = 2LW + 2LH + 2WH
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
A1 = LW
Length (L)
Wid
th (W
)Height (H)
A3 = LW
A2 = L H
A4 = L H
A 4 = W
H
A 5 =
WH
H
W
L
W
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
Example #1:• Find the surface area of a
rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
Example #1:• Find the surface area of a
rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
L = 7 W = 4cmH
= 2
.5cm
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
L = 7 W = 4cm
H =
2.5
cmExample #1:
• Find the surface area of a rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
SURFACE AREA of a Rectangular Prism
SURFACE AREA of a Rectangular Prism
Solution #1:SAr = 2LW +2WH + 2LH
SAr = 2(7cm)(4cm) + 2(4cm)(2.5cm) + 2(7cm)(2.5cm)
SAr= 56cm2 + 20cm2 + 35cm2
SAr = 111 cm2
L = 7 W = 4cm
H =
2.5
cmExample #1:
• Find the surface area of a rectangular prism whose length measures 7cm., width which measures 4cm. , and height which measures 2.5cm.
SURFACE AREA of a
Cube
SURFACE AREA of a Cube
SURFACE AREA of a Cube
SURFACE AREA of a Cube
SURFACE AREA of a Cube
Recall:
• a cube is a three-dimensional solid object bounded by six square faces.
• Area of a square is given by the formula:– A = S2
SURFACE AREA of a Cube
SURFACE AREA of a Cube
To get the surface area of a cube Sac:
SAs = S2 + S2 + S2 + S2 + S2 + S2 As = S2
As = S2
As = S2
As = S2
As = S2 As = S2
SURFACE AREA of a Cube
SURFACE AREA of a Cube
To get the surface area of a cube Sac:
SAs = S2 + S2 + S2 + S2 + S2 + S2 As = S2
As = S2
As = S2
As = S2
As = S2 As = S2
By simplifying, we get
SAs = 6S2
SURFACE AREA of a Cube
SURFACE AREA of a Cube
Example #2:
• find the surface area of a cube whose sides measure 3in.
SURFACE AREA of a Cube
SURFACE AREA of a Cube
Example #2:
• find the surface area of a cube whose sides measure 3in.
S = 3inches
SURFACE AREA of a Cube
SURFACE AREA of a Cube
Solution #2:
SA s = 6S2
SA s = 6(3in)2
SA s = 54in2
S = 3inches
Example #2:
• find the surface area of a cube whose sides measure 3in.
SURFACE AREA of a
Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
Notice:
• It has a flat base and a flat top
• The base is the same as the top, and also in-between
• Because it has a curved surface it is not a polyhedron.
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
• When we cut the body of a cylinder, we obtain a rectangle.– The formula for the area of a rectangle
(Ar) is LxW
• A right circular cylinder has 2 circular bases.– The formula for the area of a circle (Ac) is
πr2
• The length of the body of the cylinder is equal to the circumference of its circular bases.– L = 2πr– W = h (for height)
• Ar = 2πrh
Ac =πr2
Ar = 2πrh
Ac =πr2
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
To get the surface area of a right circular cylinder
SA c = 2Ac + Ar
SA c = 2πr2 + LW SA c = 2πr2 + 2πrh
Ac =πr2
Ar = 2πrh
Ac =πr2
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
To get the surface area of a right circular cylinder
SA c = 2Ac + Ar
SA c = 2πr2 + LW SA c = 2πr2 + 2πrh
By simplification, we obtain
SA c = 2πr(r + h)Ac =πr2
Ar = 2πrh
Ac =πr2
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
Example #3:
• find the surface area of a right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches.
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
Example #3:
• find the surface area of a right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches.
r = 1.5in.
h = 5.2in.
SURFACE AREA of a Right Circular Cylinder
SURFACE AREA of a Right Circular Cylinder
Solution #3:SA = 2π(r + h)SA s = 2π(1.5in.)(1.5in.+ 5.2in.)
SA s = 3πin.(6.7in.)
SA s = 201πin2
r = 1.5in.
h = 5.2in.
Example #3:
• find the surface area of a right circular cylinder with a radius of 1.5 inches and a height of 5.2 inches.
Remember
Remember
Remember
Remember
• Units count. Use the same units for all measurements.• Surface Area of any prism is given by:
Lateral area + Area of two ends
The End
