1. Splash Screen

2. Lesson Menu 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 aExample 4: Real-World Example: Volume of a SphereSphere

3. Over Lesson 12–3 5-Minute Check 1 A.47.1 yd 3 B.58.3 yd 3 C.135.5 yd 3 D.141.3 yd 3 Find the volume of the cylinder.

4. Over Lesson 12–3 5-Minute Check 2 A.75.36 m 3 B.150.8 m 3 C.162.7 m 3 D.910.1 m 3 Find the volume of the cylinder.

5. Over Lesson 12–3 5-Minute Check 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.

6. Over Lesson 12–3 5-Minute Check 4 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?

7. Over Lesson 12–3 5-Minute Check 5 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 cm 3. How many scarves can she fit into the cylinder?

8. Then/Now 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.

9. Vocabulary sphere

10. Concept A

11. Example 1 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.

12. Example 1 CYP A.112 in 3 B.168 in 3 C.336 in 3 D.448 in 3 Find the volume of the pyramid. Round to the nearest tenth if necessary.

13. Concept B

14. Example 2 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

15. Example 2 A.40.3 in 3 B.422.7 in 3 C.715.8 in 3 D.1690.7 in 3 Find the volume of the cone. Round to the nearest tenth.

16. Concept C

17. Example 3 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.  

18. Example 3 A.339.3 cm 3 B.763.4 cm 3 C.3053.6 cm 3 D.9160.9 cm 3 Find the volume of the sphere. Round to the nearest tenth.

19. Example 4 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. UnderstandYou know the beach ball has a diameter of 12 inches and a leak causes the air to escape at a rate of 1.5 cubic inches per minute. PlanFind the volume of the beach ball and how long it will take to deflate.

20. Example 4 Volume of a Sphere Solve Since d = 12, replace r with 6. Simplify. The volume is 904.8 in 3. Write the formula for the volume of a sphere.

21. Example 4 Volume of a Sphere Estimate 900 ÷ 1.5 = 600 minutes or 10 hours Write a proportion. x ≈ 603.2

22. Example 4 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. 

23. Example 4 CYP A.117.8 ft 3 ; about 78.5 min B.471.2 ft 3 ; about 314 min C.903.4 ft 3 ; about 602 min D.952 ft 3 ; 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 ft 3 per minute.

24. End of the Lesson