A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is

Question

A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?

Accepted Answer

Choice A is correct. The volume, V , of a right circular cylinder is given by the formula V = &#960; r 2 h , where &#960; r 2 is the area of the base of the cylinder and h is the height. It&rsquo;s given that a right circular cylinder has a volume of 432 cubic centimeters and the area of the base is 24 square centimeters. Substituting 432 for V and 24 for &#960; r 2 in the formula V = &#960; r 2 h yields 432 = 24 h . Dividing both sides of this equation by 24 yields 18 = h . Therefore, the height of the cylinder, in centimeters, is 18 . Choice B is incorrect. This is the area of the base, in square centimeters, not the height, in centimeters, of the cylinder. Choice C is incorrect. This is the height, in centimeters, of a cylinder if its volume is 432 cubic centimeters and the area of its base is 2 , not 24 , cubic centimeters. Choice D is incorrect. This is the height, in centimeters, of a cylinder if its volume is 432 cubic centimeters and the area of its base is 1 24 , not 24 , cubic centimeters.

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