A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 12,150π ft^3.
Radius of cylinder = (1/2)(diameter) = (1/2)(30) = 15 Volume of circular cylinder = (π)(radius^2)(height) = (π)(15^2)(height) = (225π)(height) Volume of hemisphere = (2/3)(π)(radius^3) = (2/3)(π)(15^3) = (2/3)(π)(3375) = 2250π So Silo Capacity = Volume of Cylinder + Volume of Hemisphere 12150π = (225π)(height) + 2250π Divide both sides by π 12150 = 225height + 2250 Subtract 2250 from both sides 9900 = 225height Divide both sides by 225 44 feet = height
