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Finding Volumes of Solids: Cylinder, Pyramid, and Cone Calculations

This guide explains how to find the volumes of various solids, including cylinders, pyramids, and cones. Example calculations include determining the volume of a cylinder with a radius of 2.2 meters and height of 4.5 meters, resulting in approximately 22.81 cm³. Additionally, it demonstrates calculating the side length of a square base for a pyramid with a known volume and height. The guide also provides practice problems, including a right cone with a volume of 1350π cubic meters and a radius of 18 meters to find its height.

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Finding Volumes of Solids: Cylinder, Pyramid, and Cone Calculations

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  1. 1 a. V = Bh 3 1 1 = ( 4 6)(9) 3 2 EXAMPLE 1 Find the volume of a solid Find the volume of the solid. = 36 m3

  2. b. 1 V = Bh 3 1 = (πr2)h 3 1 = (π 2.22)(4.5) 3 EXAMPLE 1 Find the volume of a solid = 7.26π ≈ 22.81 cm3

  3. 1 V = bh 3 1 2,226,450 = (x2)(144) 3 EXAMPLE 2 Use volume of a pyramid ALGEBRA Originally, the pyramid had height 144 meters and volume 2,226,450 cubic meters. Find the side length of the square base. SOLUTION Write formula. Substitute.

  4. ANSWER Originally, the side length of the base was about 215meters. EXAMPLE 2 Use volume of a pyramid 6,679,350 = 144x2 Multiply each side by 3. 46,384 ≈ x2 Divide each side by 144. 215 ≈ x Find the positive square root.

  5. ANSWER 152.42 yd3 for Examples 1 and 2 GUIDED PRACTICE Find the volume of the solid. Round your answer to two decimal places, if necessary. 1. Hexagonal pyramid

  6. 2. Right cone ANSWER 163.49m3 for Examples 1 and 2 GUIDED PRACTICE

  7. ANSWER The Height of the cone is 12.5m for Examples 1 and 2 GUIDED PRACTICE 3. The volume of a right cone is 1350πcubic meters and the radius is 18meters. Find the height of the cone.

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