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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 Lesson Menu

Find the volume of the cylinder. A. 47.1 yd3 B. 58.3 yd3 C. 135.5 yd3 D. 141.3 yd3 5-Minute Check 1

Find the volume of the cylinder. A. 75.36 m3 B. 150.8 m3 C. 162.7 m3 D. 910.1 m3 5-Minute Check 2

Find the height of a cylinder with a radius of 3 feet and a volume of 127.2 cubic feet. A. 42.4 ft B. 12.3 ft C. 4.5 ft D. 3.8 ft 5-Minute Check 3

A cylindrical bucket has a volume of about 1809 cubic inches 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? A. 24 in. B. 12 in. C. 6 in. D. 3 in. 5-Minute Check 4

Nancy uses a cylinder in her magic show 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? A. 9 B. 49 C. 98 D. 196 5-Minute Check 5

Find the volumes of pyramids and cones. 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. Then/Now

sphere Vocabulary

Concept A

Formula for volume of a pyramid Find the volume of the pyramid. Round to the nearest tenth, if necessary. Formula for volume of a pyramid The base is a square, so B = 15 ● 15. The height of the pyramid is 12 inches. Simplify. Answer: The volume is 900 cubic inches. Example 1

Find the volume of the pyramid. Round to the nearest tenth if necessary. A. 112 in3 B. 168 in3 C. 336 in3 D. 448 in3 Example 1 CYP

Concept B

Find the volume of the cone. Round to the nearest tenth. Volume of a Cone Find the volume of the cone. Round to the nearest tenth. Formula for volume of a cone Replace r with 5.5 and h with 8. V ≈ 253.4 Simplify. Answer: The volume is about 253.4 cubic meters. Example 2

Find the volume of the cone. Round to the nearest tenth. A. 40.3 in3 B. 422.7 in3 C. 715.8 in3 D. 1690.7 in3 Example 2

Concept C

Find the volume of the sphere. 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. Example 3

Find the volume of the sphere. Round to the nearest tenth. A. 339.3 cm3 B. 763.4 cm3 C. 3053.6 cm3 D. 9160.9 cm3 Example 3

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

Write the formula for the volume of a sphere. Solve Write the formula for the volume of a sphere. Since d = 12, replace r with 6. Simplify. The volume is 904.8 in3. Example 4

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

Check: 603.2 is close to the estimate of 600. The answer is correct.  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.  Example 4

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. 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 Example 4 CYP

End of the Lesson