#### Question

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2 cm ?

#### Solution

Let V be the volume of the sphere. Then,

*V *= \[\frac{4}{3}\pi r^3\]

\[\Rightarrow \frac{dV}{dr} = 4\pi r^2\]

Let S be the total surface area of sphere. Then,

*S *= \[4\pi r^2\]

\[\Rightarrow \frac{dS}{dr} = 8\pi r\]

\[\therefore \frac{dV}{dS} = \frac{\frac{dV} {dr}}{\frac{dS}{dr}}\]

\[ \Rightarrow \frac{dV}{dS} = \frac{4\pi r^2}{8\pi r} = \frac{r}{2}\]

\[ \Rightarrow \left( \frac{dV}{dS} \right)_{r = 2} = \frac{2}{2}\]

\[ = 1 cm\]

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Solution for question: Find the Rate of Change of the Volume of a Sphere with Respect to Its Surface Area When the Radius is 2 Cm. concept: Rate of Change of Bodies Or Quantities. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science