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Volume of Pyramids and Cones

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.

In fact, the volume of a pyramid is exactly one- third the volume of a prism with the same height and a congruent base. The height of a pyramid is the perpendicular distance from the pyramid’s base to the vertex opposite the base.

Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Additional Example 1A: 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.

Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Additional Example 1B: Finding the Volume of a Rectangular Pyramid V = 1313 Bh Use the formula. B = ½ · 30 · 25 = 375 Find the area of the triangular base. V = 1313 · 375 · 26 Substitute for B and h. V = 3250 ft 3 Multiply.

Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Check It Out: Example 1A

Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable. Check It Out: Example 1B

The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base.

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 2  3.14 · 5 2  78.5. Substitute for B and h. Multiply. 1313 ·  ≈ 1. 1313 V ≈ ·  5 2 · 6  150 yd 3 The answer is reasonable.

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 · 28.26 · 7 V  65.9 cm 3 Estimate Use the formula. The base is a circle so B =  · r 2  3.14 · 3 2  28.26. Substitute for B and h. Multiply. 1313 ·  ≈ 1. 1313 V ≈ ·  3 2 · 7  63 cm 3 The answer is reasonable. 7 cm 3 cm

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 2 7 cm 4 cm

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