Modded SAT Question Bank
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Test
Math
Domain
Geometry and Trigonometry
Skill
Area and volume
Difficulty
Medium
ID: 151eda3c
Modded SAT Question Bank by Abdullah Mallik

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?

  1. 16,000 pi

  2. 20,000 pi

  3. 25,000 pi

  4. 31,250 pi

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Correct Answer: B
Rationale

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.

Question Difficulty: Medium
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