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**9-3 Volume of Pyramids, Cones, and Spheres Warm Up Problem of the Day**

Course 2 Warm Up Problem of the Day Lesson Presentation

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**9-3 Volume of Pyramids, Cones, and Spheres Warm Up**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Warm Up Find each volume to the nearest tenth. Use 3.14 for . 1. cylinder: radius = 6 m, height = 11 m 1,243.4 m3 2. rectangular prism: length = 10 cm, width = 8.64 cm, height = 12.9 cm 1,114.6 cm3 3. triangular prism: base area = 34 ft2, height = 18 ft 612 ft3 4. cylinder: diameter = 8 m, height = 18 m 904.3 m3

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**9-3 Volume of Pyramids, Cones, and Spheres Problem of the Day**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Problem of the Day The volume of a 10-meter-tall square pyramid is 120 m3. What is the length of each side of the base? 6 m

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**9-3 Learn to find the volume of pyramids, cones, and spheres.**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Learn to find the volume of pyramids, cones, and spheres.

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**9-3 Volume of Pyramids, Cones, and Spheres**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres If you pour sand from a pyramid-shaped container into a prism-shaped container with the same height, base shape, and base size, you will discover an interesting relationship. The prism-shaped container appears to hold three times as much sand as the pyramid-shaped container.

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**9-3 Volume of Pyramids, Cones, and Spheres**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres In fact, the volume of a pyramid is exactly one-third the volume of a prism that has the same height, base shape, and base size as the pyramid. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex. VOLUME OF A PYRAMID The volume V of a pyramid is one-third the area of its base B times its height h. V = Bh 1 3

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**Additional Example 1A: Finding the Volume of a Pyramid**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Additional Example 1A: Finding the Volume of a Pyramid Find the volume of the pyramid. A. 1 3 3 ft V = Bh Use the formula. Find the area of the rectangular base. B = 5 · 6 = 30 6 ft 1 3 V = · 30 · 3 Substitute for B and h. 5 ft V = 30 Multiply. The volume is 30 ft3.

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**Additional Example 1B: Finding the Volume of the Pyramid**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Additional Example 1B: Finding the Volume of the Pyramid Find the volume of the pyramid. B. 1 3 V = Bh Use the formula. 1 2 Find the area of the triangular base. B = 2 · 3 = 3 1 3 Substitute for B and h. V = · 3 · 5 V = 5 Multiply. The volume is 5 cm3.

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**9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1A**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1A Find the volume of the pyramid. A. 1 3 4 ft V = Bh Use the formula. Find the area of the rectangular base. B = 9 · 7 = 63 1 3 7 ft V = · 63 · 4 Substitute for B and h. 9 ft V = 84 Multiply. The volume is 84 ft3.

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**9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1B**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1B Find the volume of the pyramid. B. 1 3 V = Bh Use the formula. h = 4 m 1 2 Find the area of the triangular base. B = 3 · 8 = 12 1 3 Substitute for B and h. V = · 12 · 4 3 m V = 16 Multiply. h = 8 m The volume is 16 m3.

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**9-3 Volume of Pyramids, Cones, and Spheres**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base. The height of a cone is the perpendicular distance from the cone’s base to its vertex. VOLUME OF A CONE The volume V of a cone is one-third the area of its base, r2, times its height h. V = r2h 1 3

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**Additional Example 2: Finding the Volume of a Cone**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Additional Example 2: Finding the Volume of a Cone Find the volume of a cone to the nearest tenth. Use 3.14 for . 1 3 V = r2h Use the formula. 1 3 V · 3.14 · 52 · 6 Substitute. V 157 Multiply. The volume is about yd3.

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**9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 2**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 2 Find the volume of a cone to the nearest tenth. Use 3.14 for . 1 3 V = r2h Use the formula. 3 yd 1 3 V · 3.14 · 22 · 3 Substitute. V 12.56 Multiply. 2 yd The volume is about 12.6 yd3.

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**9-3 Volume of Pyramids, Cones, and Spheres VOLUME OF A SPHERE**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres VOLUME OF A SPHERE The volume V of a sphere is times times the radius r cubed. V = r3 4 3 4 3

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**Additional Example 3: Finding the Volume of a Sphere**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Additional Example 3: Finding the Volume of a Sphere Find the volume of the sphere to the nearest tenth. Use 3.14 for . 4 3 V = r3 Use the formula. 4 3 V · 3.14 · 73 Substitute. V Multiply. V Round. The volume is about 1,436.0 in3.

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**9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 3**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 3 Find the volume of the sphere to the nearest tenth. Use 3.14 for . 4 3 V = r3 Use the formula. 4 in. 4 3 V · 3.14 · 43 Substitute. V Multiply. V 267.9 Round. The volume is about in3.

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**9-3 Volume of Pyramids, Cones, and Spheres Lesson Quiz**

Course 2 9-3 Volume of Pyramids, Cones, and Spheres Lesson Quiz Find the volume of each solid to the nearest tenth. Use 3.14 for . 301.4 yd3 80 ft3 3. sphere with radius 3 ft 4. 14 ft tall triangular pyramid whose base triangle has a 12 ft base and a height of 9 ft 113.0 ft3 252 ft3

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