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• lateral face
• lateral surface area• total surface area
• Find the lateral and total surface areas of prisms and cylinders.
Surface Areas of a Prism
Find the lateral and total surface area of the rectangular prism.
Area of Base
B = ℓw
B = 15(9) or 135
Perimeter of Base
P = 2ℓ + 2w
P = 2(15) + 2(9) or 48
Surface Areas of a Prism
Use this information to find the lateral and total surface area.
Answer: The lateral surface area is 336 square millimeters, and the total surface area is 606 square millimeters.
Total Surface Area
S = L + 2B
S = 336 + 2(135) or 606
Lateral Surface Area
L = Ph
L = 48(7) or 336
1. A
2. B
3. C
4. D0% 0%0%0%
A. 112 cm2
B. 126 cm2
C. 130 cm2
D. 142 cm2
Find the total surface area of the rectangular prism.
Surface Areas of a Prism
CAMPING A family wants to reinforce the fabric of its tent with a waterproofing treatment. Find the total surface area, including the floor, of the tent below.
A triangular prism consists of two congruent triangular faces and three rectangular faces.
Surface Areas of a Prism
Draw and label a net of this prism. Find the area of each face.
Answer: The surface area of the tent is about 131.1 square feet.
bottom
left side
right side
two bases
Add to find the total surface area.29 + 36.54 + 36.54 + 29 = 131.08
5 ● 5.8 = 29
6.3 ● 5.8 = 36.54
6.3 ● 5.8 = 36.54
1. A
2. B
3. C
4. D
0% 0%0%0%
A. 85.5 in2
B. 90.2 in2
C. 93.1 in2
D. 108.4 in2
DECORATING Julia is painting triangular prisms to use as decoration in her garden. Find the surface area of the prism.
Surface Areas of Cylinders
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
Answer: The lateral surface area is about 31.4 square meters, and the total surface area is about 70.7 square meters.
Total Surface AreaLateral Surface Area
L = 2πrh
L = 2π(2.5)(2)
S = L + 2πr2
S = 3.14 + 2π(2.5)2
1. A
2. B
3. C
4. D0% 0%0%0%
A. 176.4 mm2
B. 188.7 mm2
C. 207.3 mm2
D. 245.1 mm2
Find the total surface area of the cylinder. Round to the nearest tenth.
LABELS Find the area of the label on the can of juice. Round to the nearest tenth.
Since the label covers the lateral surface of the can, you only need to find the can’s lateral surface area.
Surface Areas of Cylinders
Estimate
Answer: The area of the label is about 113.1 square inches.
Surface Areas of Cylinders
113.1 Simplify.
L = 2πrh Lateral surface area of a cylinder
L = 2π(2.25)(8) r = 2.25, h = 8
1. A
2. B
3. C
4. D0% 0%0%0%
A. 132.9 in2
B. 155.5 in2
C. 164.4 in2
D. 185.2 in2
LABELS Find the area of the label on the can of juice. Round to the nearest tenth.
1. A
2. B
3. C
4. D
0% 0%0%0%
A. 15 m3
B. 20 m3
C. 40 m3
D. 60 m3
Find the volume of the given solid. Round to the nearest tenth if necessary.
(over Lesson 7-6)
1. A
2. B
3. C
4. D0% 0%0%0%
A. 1,026.3 ft3
B. 1,539.1 ft3
C. 2,931.6 ft3
D. 3,078.2 ft3
Find the volume of the given solid. Round to the nearest tenth if necessary.
(over Lesson 7-6)
1. A
2. B
3. C
4. D
0% 0%0%0%
A. 35 cm3
B. 50 cm3
C. 70 cm3
D. 105 cm3
Find the volume of the given solid. Round to the nearest tenth if necessary.
(over Lesson 7-6)
1. A
2. B
3. C
4. D0% 0%0%0%
A. 14.0 yd3
B. 28.0 yd3
C. 42.0 yd3
D. 84.0 yd3
Find the volume of a triangular pyramid if the triangle base has base 6.5 yd and height 2.25 yd, and the prism height is 5.75 yd. Round to the nearest tenth if necessary.
(over Lesson 7-6)
1. A
2. B
3. C
4. D
0% 0%0%0%
A. 7.9 in3
B. 11.8 in3
C. 35.3 in3
D. 39.3 in3
Ricky bought a box of ice cream cones. Ricky wants to know how much ice cream each cone can hold. If each cone has a diameter of 3 inches and a height of 5 inches, what is the approximate volume of each cone?
(over Lesson 7-6)
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