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?

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Accepted Answer

Choice C is correct. The volume, V, of a right circular cylinder is given by the formula V = πr 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 = πr 2 h yields V = π(11) 2 (6), which is equivalent to V = π(121)(6), or V = 726π. Therefore, the volume, in cubic centimeters, of the cylinder is 726π. 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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