Multiple choice

A cone and a cylinder have the same base radius and height. The volume of the cone is 432π cubic centimeters. What is the volume of the cylinder in cubic centimeters?

  1. 432π

  2. 864π

  3. 1,296π

  4. 1,728π
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C Correct answer
Explanation

The volume of a cone is (1/3) * pi * r^2 * h, and the volume of a cylinder is pi * r^2 * h. Since they share the same radius and height, the cylinder volume is exactly 3 times the cone volume. 3 * 432pi = 1296pi.

AI explanation

The volume of a cylinder is given by the formula pi * r^2 * h, while the volume of a cone with the same base and height is one-third of that, or (1/3) * pi * r^2 * h. Since the cone's volume is 432 pi, the cylinder's volume must be three times larger. Multiplying 432 pi by 3 gives a cylinder volume of 1,296 pi cubic centimeters.

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