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Geometry and Trigonometry Difficulty: Hard

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

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Explanation

Choice C is correct. The volume of right circular cylinder A is given by the expression pi r squared times h, where r is the radius of its circular base and h is its height. The volume of a cylinder with twice the radius and half the height of cylinder A is given by pi times, open parenthesis, 2 r, close parenthesis, squared, times one half h, which is equivalent to 4 pi r squared, times, one half h, and equals 2 pi r squared times h. Therefore, the volume is twice the volume of cylinder A, or 2 times 22, equals 44.

Choice A is incorrect and likely results from not multiplying the radius of cylinder A by 2. Choice B is incorrect and likely results from not squaring the 2 in 2r when applying the volume formula. Choice D is incorrect and likely results from a conceptual error.