Five-Minute Check (over Lesson 12–4)

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

Over Lesson 12–4

A. 324 in3

B. 224 in3

C. 162 in3

D. 108 in3

Find the volume of the figure.

Over Lesson 12–4

A. 1003.6 cm3

B. 923.6 cm3

C. 378.7 cm3

D. 126 cm3

Find the volume of the figure.

Over Lesson 12–4

A. 22.4 in3

B. 20.6 in3

C. 9.42 in3

D. 7.23 in3

Find the volume of a sphere with a radius of 1.75 inches.

Over Lesson 12–4

A. 1080 mm3

B. 960 mm3

C. 360 mm3

D. 280 mm3

Find the volume of a hexagonal pyramid with a base area of 120 mm2 and height of 9 mm.

Over Lesson 12–4

A. 8.5 in3

B. 7.5 in3

C. 6.5 in3

D. 5.5 in3

What is the volume of a cone with a radius of 1.2 inches and a height of 5 inches?

Over Lesson 12–4

A. 48 centimeters

B. 24 centimeters

C. 36 centimeters

D. 12 centimeters

A sphere and a cone have the same volume. Both have a radius of 12 centimeters. What is the approximate height of the cone?

You have already found the area of two-dimensional figures. (Lesson 11–6)

• Find lateral area and surface area of prisms.

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

• lateral face

• lateral area

• surface area

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

Answer: The lateral area is 440 square centimeters. The surface area is 1868 square centimeters.

Find the surface area.

S = L + 2B

= L + 2ℓw

= 440 + 2(34)(21)

= 1868 cm2

Surface Area of Prisms

B. Find the lateral and surface areas of the prism.

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.

The lateral area is made up of faces that are not parallel.

Surface Area of Prisms

Find the surface area.

Answer: The lateral area of the triangular prism is 144 square meters. The surface area of the triangular prism is 336 square meters.

S = L + 2BWrite the formula.

= 144 + 192 or 336 m2

Simplify.

Substitution

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

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

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

Surface Area of Prisms

One sheet of plywood covers 32 ft2 and two sheets cover 2 ● 32 or 64 ft2.

32 < 62 < 64

Answer: Alex will need at least 2 sheets of plywood.

A. 1 quart

B. 2 quarts

C. 3 quarts

D. 4 quarts

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?