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Lesson Menu
Five-Minute Check (over Lesson 124) Then/Now New
Vocabulary Key Concept Lateral and Surface Area
of Prisms Example 1 Surface Area of
Prisms Example 2 Real-World Example Surface
Area of Prisms
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5-Minute Check 1
Find the volume of the figure.
A. 324 in3 B. 224 in3 C. 162 in3 D. 108 in3
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5-Minute Check 2
Find the volume of the figure.
A. 1003.6 cm3 B. 923.6 cm3 C. 378.7 cm3 D. 126
cm3
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5-Minute Check 3
Find the volume of a sphere with a radius of
1.75 inches.
A. 22.4 in3 B. 20.6 in3 C. 9.42 in3 D. 7.23 in3
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5-Minute Check 4
Find the volume of a hexagonal pyramid with a
base area of 120 mm2 and height of 9 mm.
A. 1080 mm3 B. 960 mm3 C. 360 mm3 D. 280 mm3
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5-Minute Check 5
What is the volume of a cone with a radius of
1.2 inches and a height of 5 inches?
A. 8.5 in3 B. 7.5 in3 C. 6.5 in3 D. 5.5 in3
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5-Minute Check 6
A sphere and a cone have the same volume. Both
have a radius of 12 centimeters. What is the
approximate height of the cone?
A. 48 centimeters B. 24 centimeters C. 36
centimeters D. 12 centimeters
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Then/Now
You have already found the area of
two-dimensional figures. (Lesson 116)

• Find lateral area and surface area of prisms.

• Find surface area of real-world objects shaped
  like prisms.

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Vocabulary

• lateral face

• lateral area
• surface area

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Concept
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Example 1 A
Surface Area of Prisms
A. Find the lateral and surface areas of the
prism.
Find the lateral area. L Ph (2l
2w)(h) (2 ? 34 2 ? 21)(4) 440 cm2
Find the surface area. S L 2B L
2lw 440 2(34)(21) 1868 cm2
Answer The lateral area is 440 square
centimeters. The surface area is 1868 square
centimeters.
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Example 1 B
Surface Area of Prisms
B. Find the lateral and surface areas of the
prism.
The lateral area is made up of faces that are not
parallel.
L Ph Write the formula. (12 16 20)(3) P
is perimeter of the triangular base. h is the
height of the prism. 48 ? 3 or 144 m2 Simplify.
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Example 1 B
Surface Area of Prisms
Find the surface area.
S L 2B Write the formula.
Substitution
144 192 or 336 m2 Simplify.
Answer The lateral area of the triangular prism
is 144 square meters. The surface area of the
triangular prism is 336 square meters.
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Example 1 CYPA
A. Find the lateral area and the surface area of
the rectangular prism.
A. lateral area, 152 in2 surface area, 292
in2 B. lateral area, 182 in2 surface area, 322
in2 C. lateral area, 304 in2 surface area, 444
in2 D. lateral area, 364 in2 surface area, 560
in2
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Example 1 CYPB
B. Find the lateral area and the surface area of
the triangular prism.
A. lateral area, 19 ft2 surface area, 31
ft2 B. lateral area, 61 ft2 surface area, 96
ft2 C. lateral area, 84 ft2 surface area, 96
ft2 D. lateral area, 96 ft2 surface area, 108
ft2
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Example 2
Surface Area of Prisms
CARPENTRY Alex is building a large storage box
out of plywood. The box is a rectangular prism
measuring 5 feet long, 3 feet wide, and 2 feet
high.Find the number of sheets of plywood he
would need to buy to build the box if 1 sheet
covers 32 square feet.
Find the lateral area. L Ph (2l 2w)h
(2 ? 5 2 ? 3)2 32 ft2
Find the surface area. S L 2B L 2lw
32 2 ? 3 ? 5 32 30 or 62 ft2
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Example 2
Surface Area of Prisms
One sheet of plywood covers 32 ft2 and two sheets
cover 2 ? 32 or 64 ft2. 32 lt 62 lt 64
Answer Alex will need at least 2 sheets of
plywood.
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Example 2 CYP
Jan is painting all the sides of a rectangular
cabinet. The cabinet measures 3 feet long, 4 feet
wide, and 5 feet tall. How much paint will she
need if one quart of paint covers 50 square feet?
A. 1 quart B. 2 quarts C. 3 quarts D. 4 quarts
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End of the Lesson