A right circular cylinder has a base diameter of 22 centimeters and a height of 6 centimeters. What is the

Question

A right circular cylinder has a base diameter of 22 centimeters and a height of 6 centimeters. What is the volume, in cubic centimeters, of the cylinder?

Accepted Answer

Choice C is correct. 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. It's given that a right circular cylinder has a height of 6 centimeters. Therefore, h = 6 . It's also given that the cylinder has a base diameter of 22 centimeters. The radius of a circle is half the diameter of the circle. Since the base of a right circular cylinder is a circle, it follows that the radius of the base of the right circular cylinder is 22 2 , or 11 , centimeters. Therefore, r = 11 . Substituting 11 for r and 6 for h in the formula V = &#960; r 2 h yields V = &#960; 11 2 6 , which is equivalent to V = &#960; 121 6 , or V = 726 &#960; . Therefore, the volume, in cubic centimeters, of the cylinder is 726 &#960; . Choice A is incorrect. This is the volume of a right circular cylinder that has a base diameter of 2 22 , not 22 , centimeters and a height of 6 centimeters. Choice B is incorrect. This is the volume of a right circular cylinder that has a base diameter of 4 11 , not 22 , centimeters and a height of 6 centimeters. Choice D is incorrect. This is the volume of a right circular cylinder that has a base diameter of 44 , not 22 , centimeters and a height of 6 centimeters.

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