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The volume of a cylinder is pi*(radius)^2*height. We are not given the radius here, but we know the circumference. Circumference is 2*pi*radius. So radius is equal to the circumference/(2*pi). We can then substitute this into the equation for volume to get: V=pi*(circumference/(2*pi))^2*height=(circumference)^2/(4*pi)*height.
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For your problem we have circumference=84 inches and height=32 inches. So:
(84 inches)^2/(4*pi)*32 inches=7056 square inches/(4*pi)*32 inches=1764 square inches/pi*32 inches=56448 cubic inches/pi=17967.9564553 cubic inches which is about 17968 cubic inches.
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