Splash Screen. 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.

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Splash Screen

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

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

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

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 cubic feet.

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?

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?

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.

Vocabulary sphere

Concept A

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.

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.

Concept B

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

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

Concept C

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 cubic feet.  

Example 3 A cm 3 B cm 3 C cm 3 D cm 3 Find the volume of the sphere. Round to the nearest tenth.

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.

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

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

Example 4 Volume of a Sphere Answer: It will take about minutes or about 10 hours for the beach ball to deflate. Check: is close to the estimate of 600. The answer is correct. 

Example 4 CYP A ft 3 ; about 78.5 min B ft 3 ; about 314 min C 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.

End of the Lesson