A right circular cylinder has a volume of 377 cubic centimeters. The area of the base of the cylinder is

Question

A right circular cylinder has a volume of 377 cubic centimeters. The area of the base of the cylinder is 13 square centimeters. What is the height, in centimeters, of the cylinder?

Accepted Answer

The correct answer is 29 . The volume, V , of a right circular cylinder is given by the formula V = &#960; r 2 h , where r is the radius of the base of the cylinder and h is the height of the cylinder. Since the base of the cylinder is a circle with radius r , the area of the base of the cylinder is &#960; r 2 . It's given that a right circular cylinder has a volume of 377 cubic centimeters; therefore, V = 377 . It's also given that the area of the base of the cylinder is 13 square centimeters; therefore, &#960; r 2 = 13 . Substituting 377 for V and 13 for &#960; r 2 in the formula V = &#960; r 2 h yields 377 = 13 h . Dividing both sides of this equation by 13 yields 29 = h . Therefore, the height of the cylinder, in centimeters, is 29 .

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