1. Splash Screen

2. Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards.
A yd3
B yd3
C yd3
D yd3
5-Minute Check 5

3. The volume of a triangular prism is 655 cubic feet
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.
A ft2
B. 131 ft2
C. 650 ft2
D. 660 ft2
5-Minute Check 6

4. Mathematical Practices
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.
CCSS

5. You found surface areas of pyramids and cones.
Find volumes of pyramids.
Find volumes of cones.
Then/Now

6. Concept

7. Find the volume of the square pyramid.
Volume of a Pyramid
Find the volume of the square pyramid.
Volume of a pyramid
s 3, h 7 21
Multiply.
Answer: The volume of the pyramid is 21 cubic inches.
Example 1

8. Brad is building a model pyramid for a social studies project
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.
Example 1

9. Concept

10. A. Find the volume of the oblique cone to the nearest tenth.
Volume of a Cone
A. Find the volume of the oblique cone to the nearest tenth.
Example 2A

11. Answer: The volume of the cone is approximately 2168.0 cubic feet.
Volume of a Cone
Volume of a cone
r = 9.1, h = 25 ≈
Use a calculator.
Answer: The volume of the cone is approximately cubic feet.
Example 2A

12. B. Find the volume of the cone to the nearest tenth.
Volume of a Cone
B. Find the volume of the cone to the nearest tenth.
Example 2B

13. Answer: The volume of the cone is approximately 314.2 cubic inches.
Volume of a Cone
Volume of a cone
r = 5, h = 12
≈ 314.2
Use a calculator.
Answer: The volume of the cone is approximately cubic inches.
Example 2B

14. A. Find the volume of the oblique cone to the nearest tenth.
A m3
B. 27,463.2 m3
C m3
D m3
Example 2A

15. B. Find the volume of the cone to the nearest tenth.
A m3
B m3
C m3
D m3
Example 2B

16. Answer: The volume of the pyramidion is 22,680 cubic centimeters.
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
B = 36 ● 36, h = 52.5
Simplify.
Answer: The volume of the pyramidion is 22,680 cubic centimeters.
Example 3

17. 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
Example 3

18. Concept

19. End of the Lesson