Splash Screen

Chapter 7Lesson 7-7

1. A2. B3. C4. D

A. face

B. vertex

C. base

D. edge

Which of the following is represented by a point?

(over Lesson 7-4)

A. AB. BC. CD. D

(over Lesson 7-5)

The base of the triangle of a triangular prism is 3 yd, the altitude is 5 yd, and

the height is 9 yd. Find the volume of the triangular prism. Round to the

nearest tenth if necessary.

A. yd3 B. yd3

C. yd3 D. yd3

A. AB. BC. CD. D

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. A2. B3. C4. D

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)

• lateral face

• lateral surface area

• Find the lateral and total surface areas of prisms and cylinders.

• total surface area

Please go to page 386 in your math textbook and write the definitions onto your student-built glossary for the “New Vocabulary”.

Standard 7MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

Standard 7MG3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.

1) Take out the clear plastic rectangular prism at your table.

2) Your task is to determine the amount of material needed to completely cover the prism.

3) When measuring, use centimeters and millimeters.

4) Write down each step you take on a response board.

Team Challenge

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

A. AB. BC. CD. D

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. A2. B3. C4. D

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.

L = πdh

S = πdh + 2πr2

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 = π d h

L = (3.14) (5) (2)

1. A2. B3. C4. D

A. 176.4 mm2

B. 188.7 mm2

C. 207.2 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 113.0 square inches.

Surface Areas of Cylinders

113.0

L = π d h

L = (3.14) (4.5) (8) d = 4.5; h = 8

A. AB. BC. CD. D

A. 132.9 in2

B. 155.4 in2

C. 164.4 in2

D. 185.2 in2

LABELS Find the lateral area of the label on the can of juice. Round to the nearest tenth.

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