Five-Minute Check (over Lesson 12–4)

CCSS

Then/Now

Key Concept: Volume of a Pyramid

Example 1: Volume of a Pyramid

Key Concept: Volume of a Cone

Example 2: Volume of a Cone

Example 3: Real-World Example: Find Real-World Volumes

Concept Summary: Volumes of Solids

Over Lesson 12–4

A. 240 in3

B. 200 in3

C. 120 in3

D. 100 in3

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

Over Lesson 12–4

A. 240 in3

B. 200 in3

C. 120 in3

D. 100 in3

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

Over Lesson 12–4

A. 785.4 cm3

B. 547.3 cm3

C. 314.2 cm3

D. 157.1 cm3

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

Over Lesson 12–4

A. 785.4 cm3

B. 547.3 cm3

C. 314.2 cm3

D. 157.1 cm3

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

Over Lesson 12–4

A. 627.5 m3

B. 843.4 m3

C. 986.4 m3

D. 1017.9 m3

What is the volume of the cylinder. Round to the nearest tenth if necessary.

Over Lesson 12–4

A. 627.5 m3

B. 843.4 m3

C. 986.4 m3

D. 1017.9 m3

What is the volume of the cylinder. Round to the nearest tenth if necessary.

Over Lesson 12–4

A. 225.4 ft3

B. 203.7 ft3

C. 183.8 ft3

D. 152.8 ft3

What is the volume of the prism? Round to the nearest tenth if necessary.

Over Lesson 12–4

A. 225.4 ft3

B. 203.7 ft3

C. 183.8 ft3

D. 152.8 ft3

What is the volume of the prism? Round to the nearest tenth if necessary.

Over Lesson 12–4

A. 1110 yd3

B. 1227 yd3

C. 1512 yd3

D. 2012 yd3

Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards.

Over Lesson 12–4

A. 1110 yd3

B. 1227 yd3

C. 1512 yd3

D. 2012 yd3

Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards.

Over Lesson 12–4

A. 65.5 ft2

B. 131 ft2

C. 650 ft2

D. 660 ft2

The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base.

Over Lesson 12–4

A. 65.5 ft2

B. 131 ft2

C. 650 ft2

D. 660 ft2

The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base.

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 pyramids and cones.

• Find volumes of pyramids.

• Find volumes of cones.

Volume of a Pyramid

Find the volume of the square pyramid.

Answer:

Volume of a pyramid

Multiply. 21

s 3, h 7

Volume of a Pyramid

Find the volume of the square pyramid.

Answer: The volume of the pyramid is 21 cubic inches.

Volume of a pyramid

Multiply. 21

s 3, h 7

Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.

A. 416 ft3

B.

C.

D.

Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.

A. 416 ft3

B.

C.

D.

Volume of a Cone

A. Find the volume of the oblique cone to the nearest tenth.

Volume of a Cone

Answer:

Use a calculator.

Volume of a cone

r = 9.1, h = 25

≈ 2168.0

Volume of a Cone

Answer: The volume of the cone is approximately 2168.0 cubic feet.

Use a calculator.

Volume of a cone

r = 9.1, h = 25

≈ 2168.0

Volume of a Cone

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

Volume of a Cone

Answer:

Use a calculator.

Volume of a cone

r = 5, h = 12

≈ 314.2

Volume of a Cone

Answer: The volume of the cone is approximately 314.2 cubic inches.

Use a calculator.

Volume of a cone

r = 5, h = 12

≈ 314.2

A. 444.4 m3

B. 27,463.2 m3

C. 3051.5 m3

D. 9154.4 m3

A. Find the volume of the oblique cone to the nearest tenth.

A. 444.4 m3

B. 27,463.2 m3

C. 3051.5 m3

D. 9154.4 m3

A. Find the volume of the oblique cone to the nearest tenth.

A. 3015.9 m3

B. 125.7 m3

C. 1005.3 m3

D. 251.3 m3

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

A. 3015.9 m3

B. 125.7 m3

C. 1005.3 m3

D. 251.3 m3

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

Find Real-World Volumes

SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Volume of a pyramid

Answer:

B = 36 ● 36, h = 52.5

Simplify.

Find Real-World Volumes

SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Volume of a pyramid

Answer: The volume of the pyramidion is 22,680 cubic centimeters.

B = 36 ● 36, h = 52.5

Simplify.

A. 18,775 cm3

B. 19,500 cm3

C. 20,050 cm3

D. 21,000 cm3

SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

A. 18,775 cm3

B. 19,500 cm3

C. 20,050 cm3

D. 21,000 cm3

SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.