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1 Consider a prism and a pyramid that have the same base area and the same height. If you completely fill the pyramid with sand and pour the sand into the prism, youll find that the sand fills one third of the prism. You can conclude that the volume of the pyramid is one third of the volume of the prism. The same relationship holds for a cylinder and a cone with the same base area and the same height. Volumes of Pyramids and Cones 10.8 LESSON

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2 Volume of a Pyramid or a Cone The volume V of a pyramid or a cone is one third of the product of the base area B and the height h. Words Algebra V = Bh 1313 Volumes of Pyramids and Cones 10.8 LESSON

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3 EXAMPLE 1 Finding the Volume of a Pyramid The base of a pyramid is a square. The side length of the square is 24 feet. The height of the pyramid is 9 feet. Find the volume of the pyramid. Write formula for volume of a pyramid. Substitute 24 2 for B and 9 for h. Simplify. ANSWER The volume of the pyramid is 1728 cubic feet. V = Bh 1313 = 1728 = (24 2 )(9) 1313 Volumes of Pyramids and Cones 10.8 LESSON

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4 EXAMPLE 2 Finding the Volume of a Cone Find the volume of the cone shown. Round to the nearest cubic millimeter. Write formula for volume of a cone. Substitute 6.75 for r and 10 for h. Evaluate. Use a calculator. The radius is one half of the diameter, so r = V = πr 2 h 1313 = π(6.75) 2 (10) ANSWER The volume of the cone is about 477 cubic millimeters. Volumes of Pyramids and Cones 10.8 LESSON

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5 EXAMPLE 3 Finding the Volume of a Solid Silos The grain silo shown is composed of a cylinder and a cone. Find the volume of the silo to the nearest cubic foot. 1 Find the volume of the cylindrical section. The radius is one half of the diameter, so r = 9. Write formula for volume of a cylinder. Substitute values. Then simplify. V = πr 2 h = π(9) 2 (29) 2 Find the volume of the conical section. V = πr 2 h 1313 = π(9) 2 (7) 1313 = 2349π = 189π Write formula for volume of a cone. Substitute 9 for r and 7 for h. Then simplify. Volumes of Pyramids and Cones 10.8 LESSON

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6 EXAMPLE 3 Finding the Volume of a Solid Silos The grain silo shown is composed of a cylinder and a cone. Find the volume of the silo to the nearest cubic foot. 3 Find the sum of the volumes. 2349π + 189π =2538π ANSWER The volume of the silo is about 7973 cubic feet. Volumes of Pyramids and Cones 10.8 LESSON

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7 Surface Areas and Volumes of Solids SUMMARY Prism ConePyramid CylinderSurface Area S = 2B + Ph Surface Area S = πr 2 + πrl Surface Area S = 2πr 2 + 2πrh Volume V = Bh Volume V = πr 2 h Surface Area S = B + Pl 1212 Volume V = Bh 1313 Volume V = πr 2 h 1313 Volumes of Pyramids and Cones 10.8 LESSON

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