A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of

Question

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

A.

$16,000 pi$

B.

$20,000 pi$

C.

$25,000 pi$

D.

$31,250 pi$

Accepted Answer

Choice B is correct. If the radius of container A is 16 centimeters and the radius of container B is 25% longer than the radius of container A, then the radius of container B is centimeters. The volume of a cylinder is , where r is the radius of the cylinder and h is its height. Substituting and into yields that the volume of cylinder B is cubic centimeters. Choice A is incorrect and may result from multiplying the radius of cylinder B by the radius of cylinder A rather than squaring the radius of cylinder B. Choice C is incorrect and may result from multiplying the radius of cylinder B by 25 rather than squaring it. Choice D is incorrect and may result from taking the radius of cylinder B to be 25 centimeters rather than 20 centimeters.

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