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(D) Let the radius of the sphere and the cylinder be $r$. Let the height of the cylinder be $h$. Given that the volumes are equal: Volume of sphere =

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$50$

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(D) Let the radius of the sphere and the cylinder be $r$. Let the height of the cylinder be $h$. Given that the volumes are equal: Volume of sphere = $\frac{4}{3} \pi r^3$ Volume of cylinder = $\pi r^2 h$ Equating the two: $\frac{4}{3} \pi r^3 = \pi r^2 h$ $h = \frac{4}{3} r$ The diameter of the cylinder is $d = 2r$. We need to find the percentage by which the diameter exceeds the height: Difference = $d - h = 2r - \frac{4}{3} r = \frac{2}{3} r$ Percentage = $\frac{d - h}{h} 	imes 100 = \frac{(2/3)r}{(4/3)r} 	imes 100 = \frac{2}{4} 	imes 100 = 50\%$.

$A$ sphere and a cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

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