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Volume of Pyramids, Cones, and Spheres. 9-3. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Volume of Pyramids, Cones, and Spheres. 9-3. Course 2. Warm Up Find each volume to the nearest tenth. Use 3.14 for  . 1. cylinder: radius = 6 m, height = 11 m. 1,243.4 m 3.

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9-3

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  1. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 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

  3. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 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

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

  5. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 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.

  6. Volume of Pyramids, Cones, and Spheres 9-3 1 3 Course 2 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.

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

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

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

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

  11. Volume of Pyramids, Cones, and Spheres 9-3 1 3 Course 2 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.

  12. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 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 r2h V = Use the formula. 1 3 · 3.14 · 52 · 6 Substitute. V  Multiply. V  157 The volume is about 157.0 yd3.

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

  14. Volume of Pyramids, Cones, and Spheres 9-3 4 4 3 3 Course 2

  15. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 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 r3 Use the formula. V = 4 3 · 3.14 · 73 Substitute. V  Multiply. V  1436.026 Round. V  1436.0 The volume is about 1,436.0 in3.

  16. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 Try This: Example 3 Find the volume of the sphere to the nearest tenth. Use 3.14 for . 4 3 r3 Use the formula. V = 4 in. 4 3 · 3.14 · 43 Substitute. V  Multiply. V  267.946 Round. V  267.9 The volume is about 267.9 in3.

  17. Volume of Pyramids, Cones, and Spheres 9-3 Course 2 Lesson Quiz Find the volume of each solid to the nearest tenth. Use 3.14 for . 301.4 yd3 1. 2. 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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