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Learn to find the volume of pyramids and cones.

10-3. Volume of Pyramids and Cones. Course 2. Learn to find the volume of pyramids and cones. 10-3. Volume of Pyramids and Cones. Course 2.

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Learn to find the volume of pyramids and cones.

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  1. 10-3 Volume of Pyramids and Cones Course 2 Learn to find the volume of pyramids and cones.

  2. 10-3 Volume of Pyramids and Cones Course 2 Suppose you have a square-pyramid-shaped container and a square-prism-shaped container, and the bases and heights are the same size. If you pour sand from the pyramid into the prism, it appears that the prism holds three times as much sand as the pyramid.

  3. 10-3 Volume of Pyramids and Cones Course 2 In fact, the volume of a pyramid is exactly one-third the volume of a prism if they have the same height and same-size base. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex.

  4. 10-3 Volume of Pyramids and Cones Course 2 Additional Example 1: Finding the Volume of a Rectangular Pyramid Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. 4 ft Find the area of the rectangular base. B = 5 · 7 = 35 1 3 V = · 35 · 4 Substitute for B and h. 7 ft 5 ft Multiply. V ≈ 46.7 ft3 1 3 V = Round the measurements. · 30 · 5 Estimate The answer is reasonable. V = 50 ft3

  5. 10-3 Volume of Pyramids and Cones Course 2 Check It Out: Example 1 Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. 1 3 V = Bh Use the formula. 4 ft Find the area of the rectangular base. B = 8 · 7 = 56 1 3 V = · 56 · 4 Substitute for B and h. 7 ft 8 ft Multiply. V ≈ 74.7 ft3 1 3 V = Estimate Round the measurements. · 60 · 4 The answer is reasonable. V = 80 ft3

  6. 10-3 Volume of Pyramids and Cones 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.

  7. 10-3 Volume of Pyramids and Cones 1 3 ·52 ·6 · ≈ 1. V ≈ Course 2 Additional Example 2A: Finding the Volume of a Cone Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Use the formula. The base is a circle so B = ·r2 3.14 · 52  78.5. Bh V = 1 3 Substitute for B and h. · 78.5 · 6 V  V  157 yd3 Multiply. 1 3 Estimate  150 yd3 The answer is reasonable.

  8. 10-3 Volume of Pyramids and Cones 7 cm 3 cm 1 3 ·32 ·7 · ≈ 1. V ≈ Course 2 Additional Example 2B: Finding the Volume of a Cone Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Use the formula. The base is a circle so B = ·r2 3.14 · 32  28.26. Bh V = 1 3 Substitute for B and h. · 28.26 · 7 V  V  65.9 cm3 Multiply. 1 3 Estimate  63 cm3 The answer is reasonable.

  9. 10-3 Volume of Pyramids and Cones 3 yd 2 yd 1 3 ·22 ·3 · ≈ 1. V ≈ Course 2 Check It Out: Example 2A Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Use the formula. The base is a circle so B = ·r2 3.14 · 32  12.56. Bh V = 1 3 Substitute for B and h. · 12.56 · 3 V  V = 12.56 yd3 Multiply. 1 3 Estimate  12 yd3 The answer is reasonable.

  10. 10-3 Volume of Pyramids and Cones 4 2 Use the formula. The base is a circle so B = ·r2 3.14 ·2  12.56. 7 cm 4 cm 1 3 ·22 ·7 · ≈ 1. V ≈ Course 2 Check It Out: Example 2B Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable. 1 3 Bh V = 1 3 Substitute for B and h. · 12.56 · 7 V  V  29.3 cm3 Multiply. 1 3 Estimate  28 cm3 The answer is reasonable.

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