1. Volumes of Pyramids and Cones
LESSON 12–5
Volumes of Pyramids and Cones

2. Five-Minute Check (over Lesson 12–4) TEKS 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
Lesson Menu

3. Find the volume of the prism. Round to the nearest tenth if necessary.
A. 240 in3
B. 200 in3
C. 120 in3
D. 100 in3
5-Minute Check 1

4. Find the volume of the cylinder
Find the volume of the cylinder. Round to the nearest tenth if necessary.
A cm3
B cm3
C cm3
D cm3
5-Minute Check 2

5. What is the volume of the cylinder
What is the volume of the cylinder. Round to the nearest tenth if necessary.
A m3
B m3
C m3
D m3
5-Minute Check 3

6. What is the volume of the prism
What is the volume of the prism? Round to the nearest tenth if necessary.
A ft3
B ft3
C ft3
D ft3
5-Minute Check 4

7. 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

8. 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

9. Mathematical Processes G.1(D), G.1(E)
Targeted TEKS
G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change.
G.11(D) Apply the formulas for the volume of three-dimensional
figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
Mathematical Processes
G.1(D), G.1(E)
TEKS

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

11. Concept

12. 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

13. 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

14. Concept

15. 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

16. 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

17. 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

18. 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

19. 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

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

21. 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

22. 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

23. Concept

24. Volumes of Pyramids and Cones
LESSON 12–5
Volumes of Pyramids and Cones