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Question
Find the rate of change of the volume of a sphere with respect to its diameter ?
Solution
Let V and r be the volume and diameter of the sphere, respectively. Then,
V = \[\frac{4}{3}\pi \left( \text {P radius } \right)^3\]
\[\Rightarrow \frac{dV}{dr} = \frac{1}{2}\pi r^2 \]
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