Five-Minute Check (over Lesson 12–3)

Then/Now

New Vocabulary

Key Concept: Volume of a Pyramid

Example 1: Volume of a Pyramid

Key Concept: Volume of a Cone

Example 2: Volume of a Cone

Key Concept: Volume of a Sphere

Example 3: Volume of a Sphere

Example 4: Real-World Example: Volume of a Sphere

Over Lesson 12–3

A. 47.1 yd3

B. 58.3 yd3

C. 135.5 yd3

D. 141.3 yd3

Find the volume of the cylinder.

Over Lesson 12–3

A. 75.36 m3

B. 150.8 m3

C. 162.7 m3

D. 910.1 m3

Find the volume of the cylinder.

Over Lesson 12–3

A. 42.4 ft

B. 12.3 ft

C. 4.5 ft

D. 3.8 ft

Find the height of a cylinder with a radius of 3 feet and a volume of 127.2 cubic feet.

Over Lesson 12–3

A. 24 in.

B. 12 in.

C. 6 in.

D. 3 in.

A cylindrical bucket has a volume of about 1809 cubic inches. The bucket is 16 inches high. What is the length of the diameter of the bucket?

Over Lesson 12–3

A. 9

B. 49

C. 98

D. 196

Nancy uses a cylinder in her magic show. The cylinder has a diameter of 21.5 centimeters and a height of 26 centimeters. In her act, Nancy fills the cylinder with scarves. Each scarf fills a volume of 192 cm3. How many scarves can she fit into the cylinder?

You have already found the volumes of prisms and cylinders. (Lessons 12–2 and 12–3)

• Find the volumes of pyramids and cones.

• Find the volumes of spheres.

• sphere

Volume of a Pyramid

Find the volume of the pyramid. Round to the nearest tenth, if necessary.

Formula for volume of a pyramid

Answer: The volume is 900 cubic inches.

The base is a square, so B = 15 ● 15.

The height of the pyramid is 12 inches.

Simplify.

A. 112 in3

B. 168 in3

C. 336 in3

D. 448 in3

Find the volume of the pyramid. Round to the nearest tenth if necessary.

Volume of a Cone

Find the volume of the cone. Round to the nearest tenth.

Answer: The volume is about 253.4 cubic meters.

Formula for volume of a cone

Replace r with 5.5 and h with 8.

Simplify.V ≈ 253.4

A. 40.3 in3

B. 422.7 in3

C. 715.8 in3

D. 1690.7 in3

Find the volume of the cone. Round to the nearest tenth.

Volume of a Sphere

Find the volume of the sphere. Round to the nearest tenth.

Answer: The volume of the sphere is about 523.6 cubic feet.

A. 339.3 cm3

B. 763.4 cm3

C. 3053.6 cm3

D. 9160.9 cm3

Find the volume of the sphere. Round to the nearest tenth.

Volume of a Sphere

BEACH BALL A spherical beach ball has a diameter of 12 inches. Find the volume of the beach ball. Then find how long it would take to deflate the beach ball from a slow leak, if the leak lets air escape at the rate of 1.5 cubic inches per minute. Round answers to the nearest tenth.

Understand You know the beach ball has adiameter of 12 inches and a leakcauses the air to escape at a rate of1.5 cubic inches per minute.

Plan Find the volume of the beach ball andhow long it will take to deflate.

Volume of a Sphere

Solve

Since d = 12, replace r with 6.

Simplify.

The volume is 904.8 in3.

Write the formula for the volume of a sphere.

Volume of a Sphere

Estimate 900 ÷ 1.5 = 600 minutes or 10 hours

Write a proportion.

x ≈ 603.2

Volume of a Sphere

Answer: It will take about 603.2 minutes or about 10 hours for the beach ball to deflate.

Check: 603.2 is close to the estimate of 600. The answer is correct.

A. 117.8 ft3; about 78.5 min

B. 471.2 ft3; about 314 min

C. 903.4 ft3; about 602 min

D. 952 ft3; about 628 min

When mulch was dumped from a truck, it formed a cone-shaped mound with a diameter of 15 feet and a height of 8 feet. Find the volume of the mound. Then find how long it would take for the pile to be completely removed if a person shovels the mulch at a rate of 1.5 ft3 per minute.