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Solution for Find the Rate of Change of the Volume of a Sphere with Respect to Its Surface Area When the Radius is 2 Cm. - CBSE (Commerce) Class 12 - Mathematics

ConceptRate of Change of Bodies Or Quantities

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,

= $\frac{4}{3}\pi r^3$

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

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

= $4\pi r^2$

$\Rightarrow \frac{dS}{dr} = 8\pi r$

$\therefore \frac{dV}{dS} = \frac{\frac{dV} {dr}}{\frac{dS}{dr}}$

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

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

$= 1 cm$

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Solution 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.
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