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Geometry and Trigonometry Difficulty: Medium

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?

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Explanation

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 $16 plus, 0 point 2 5 times 16, equals 20$ centimeters. The volume of a cylinder is $pi, times r squared, times h$ , where r is the radius of the cylinder and h is its height. Substituting $r equals 20$ and $h equals 50$ into $pi, times r squared, times h$ yields that the volume of cylinder B is $pi times open parenthesis, 20, close parenthesis, squared, times 50, equals 20,000 pi$ 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.