Give the dimensions of a cone and a cylinder that have the same volume. Show tha

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Mar 20th, 2015

The volume of a cylinder is V_cyl = pi* R^2 * H, where R is the radius of the base and H is the height of the cylinder. The volume of a cone is V_cone = (pi/3) * R^2 * H under similar assumptions. Suppose that a cylinder and a cone have the same radius and the height of the cone is three times the height of the cylinder. Then their volumes are equal. For example, if R = 1 m, H_cyl = 1 m, and H_cone = 3 m, then the volume of both solids is pi * 1^2 * 1 = (pi/3)*1^2*3 = 3.14... m^2.

Mar 20th, 2015

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