The radius and height of a cylinder are equal to the radius of sphere. The ratio of the rates of change of the volume of the sphere and cylinder is

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3 : 2

3 : 4

2 : 3

4 : 3

answer is A.

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Detailed Solution

$\begin{matrix} h = R r = R \\ Volume of Cylinder \\ V = {πr}^{2} h = {πR}^{3} \end{matrix} \begin{matrix} Volume of Cylender S = \frac{π}{3} {πR}^{3} \\ S = r (\frac{4}{3}) \\ \frac{\frac{dv}{dt}}{\frac{ds}{dt}} = \frac{3}{4} \end{matrix}$

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