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

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Presentation on theme: "Learn to find the volume of pyramids and cones. Course 2 10-3 Volume of Pyramids and Cones."— Presentation transcript:

1 Learn to find the volume of pyramids and cones. Course Volume of Pyramids and Cones

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. Course Volume of Pyramids and Cones

3 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 pyramids base to its vertex. Course Volume of Pyramids and Cones

4 Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Additional Example 1: Finding the Volume of a Rectangular Pyramid V = 1313 Bh Use the formula. B = 5 · 7 = 35 Find the area of the rectangular base. V = 1313 · 35 · 4 Substitute for B and h. V 46.7 ft 3 Estimate 5 ft 7 ft 4 ft Multiply. V = 1313 · 30 · 5 Round the measurements. V = 50 ft 3 The answer is reasonable. Course Volume of Pyramids and Cones

5 Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Check It Out: Example 1 V = 1313 Bh Use the formula. B = 8 · 7 = 56 Find the area of the rectangular base. V = 1313 · 56 · 4 Substitute for B and h. V 74.7 ft 3 Estimate Multiply. V = 1313 · 60 · 4 Round the measurements. V = 80 ft 3 The answer is reasonable. Course Volume of Pyramids and Cones 8 ft 7 ft 4 ft

6 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 cones base to its vertex. Course Volume of Pyramids and Cones

7 Find the volume of the cone to the nearest tenth. Use 3.14 for. Estimate to check whether the answer is reasonable. Additional Example 2A: Finding the Volume of a Cone V = 1313 Bh V 1313 · 78.5 · 6 V 157 yd 3 Estimate Use the formula. The base is a circle so B = · r · Substitute for B and h. Multiply. Course Volume of Pyramids and Cones 1313 · V · 5 2 · yd 3 The answer is reasonable.

8 Find the volume of the cone to the nearest tenth. Use 3.14 for. Estimate to check whether the answer is reasonable. Additional Example 2B: Finding the Volume of a Cone V = 1313 Bh V 1313 · · 7 V 65.9 cm 3 Estimate Use the formula. The base is a circle so B = · r · Substitute for B and h. Multiply. Course Volume of Pyramids and Cones 1313 · V · 3 2 · 7 63 cm 3 The answer is reasonable. 7 cm 3 cm

9 Find the volume of the cone to the nearest tenth. Use 3.14 for. Estimate to check whether the answer is reasonable. Check It Out: Example 2A V = 1313 Bh V 1313 · · 3 V = yd 3 Estimate Use the formula. The base is a circle so B = · r · Substitute for B and h. Multiply. Course Volume of Pyramids and Cones 1313 · V · 2 2 · 3 12 yd 3 The answer is reasonable. 3 yd 2 yd

10 Find the volume of the cone to the nearest tenth. Use 3.14 for. Estimate to check whether the answer is reasonable. Check It Out: Example 2B V = 1313 Bh V 1313 · · 7 V 29.3 cm 3 Estimate Substitute for B and h. Multiply. Course Volume of Pyramids and Cones 1313 · V · 2 2 · 7 28 cm 3 The answer is reasonable. 7 cm 4 cm Use the formula. The base is a circle so B = · r ·


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