Five-Minute Check (over Lesson 12–3)

CCSS

Then/Now

Key Concept : Volume of a Prism

Example 1: Volume of a Prism

Key Concept: Volume of a Cylinder

Example 2: Volume of a Cylinder

Key Concept: Cavalieri’s Principle

Example 3: Volume of an Oblique Solid

Example 4: Standardized Test Example: Comparing Volumes of Solids

Over Lesson 12–3

A. 600 in2

B. 623.2 in2

C. 635.3 in2

D. 647.4 in2

Find the surface area of the regular pyramid.

Over Lesson 12–3

A. 628.3 ft2

B. 642.3 ft2

C. 677.8 ft2

D. 753.9 ft2

Find the surface area of the cone.

Over Lesson 12–3

A. 420 ft2

B. 480 ft2

C. 679.8 ft2

D. 710 ft2

Find the surface area of the regular pyramid.

Over Lesson 12–3

A. 214.2 m2

B. 221.0 m2

C. 233.4 m2

D. 247.5 m2

Find the surface area of the cone.

Over Lesson 12–3

A. 80 ft2

B. 200 ft2

C. 240 ft2

D. 260 ft2

Find the surface area of a square pyramid with base length of 10 feet and slant height of 8 feet.

Over Lesson 12–3

A. 204.2 cm2

B. 282.7 cm2

C. 408.4 cm2

D. 722.6 cm2

Find the lateral area of a cone with a diameter length of 10 centimeters and a slant height of 13 centimeters. Round your answer to the nearest tenth.

Content Standards

G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Mathematical Practices

1 Make sense of problems and persevere in solving them.

7 Look for and make use of structure.

You found surface areas of prisms and cylinders.

• Find volumes of prisms.

• Find volumes of cylinders.

Volume of a Prism

Answer: The volume of the prism is 1500 cubic centimeters.

V Bh Volume of a prism

1500 Simplify.

Find the volume of the prism.

A. 6480 in3

B. 8100 in3

C. 3240 in3

D. 4050 in3

Find the volume of the prism.

Volume of a Cylinder

Find the volume of the cylinder to the nearest tenth.

Answer: The volume is approximately 18.3 cm3.

Volume of a cylinder

≈ 18.3 Use a calculator.

= (1.8)2(1.8) r = 1.8 and h = 1.8

A. 62.8 cm3

B. 628.3 cm3

C. 125.7 cm3

D. 1005.3 cm3

Find the volume of the cylinder to the nearest tenth.

Volume of an Oblique Solid

Find the volume of the oblique cylinder to the nearest tenth.

To find the volume, use the formula for a right cylinder.

Answer: The volume is approximately 17,671.5 cubic feet.

Volume of a cylinder

Use a calculator.

r 15, h 25

A. 1520.5 cm3

B. 16,725.8 cm3

C. 5324 cm3

D. 8362.9 cm3

Find the volume of the oblique cylinder to the nearest tenth.

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A,what is the length of each prism?

A 12 B 8

C 4 D 3.5

Prism A Prism B

Comparing Volumes of Solids

Read the Test Item

You know the volume of each solid and that the difference between their volumes is 128 cubic inches.

Solve the Test Item

Volume of Prism B –

Volume of Prism A = 128 Write an equation.

4x ● 9 – 4x ● 5 = 128 Use V = Bh.

16x = 128 Simplify.

x = 8 Divide each side by 16.

Answer: The length of each prism is 8 inches. The correct answer is B.

Comparing Volumes of Solids

A. 4 in.

B. 6 in.

C. 8 in.

D. 10.5 in.

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A,what is the length of each prism?

Prism A

Prism B