If the ratio of the volumes of two right circular cylinders

Hi All,

We're told that two right circular cylinders have the SAME height and the ratio of their volumes is given by 64/9. We're asked for the ratio of their radii.

Volume of a cylinder = (pi)(R^2)(H)

Since the cylinders have the SAME height, that value (whatever it is) doesn't impact the ratio of the two volumes. Thus, the ratio is completely depended on the radius of each cylinder (specifically, radius-squared). Thus, we're looking for the square-roots of 64 and 9. That would be 8 and 3, respectively.

We can prove that this is the correct answer with the following example:
1st cylinder: radius = 8, height = 1, Volume = (pi)(64)(1) = 64pi
2nd cylinder: radius = 3, height = 1, Volume = (pi)(9)(1) = 9pi
64pi:9pi = 64/9

Final Answer: B

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