The rate of change of volume of sphere with respect to its radius is ___________ when its radius is $r = 7$ cm.

166 π c m^{3} / c m

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196 π c m^{3} / c m

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169 π c m^{2} / c m

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196 π c m / c m^{3}

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Solution

The correct option is B $196 π c m^{3} / c m$
$\to$ V $=$ Volume of Sphere
$= \frac{4}{3} π r^{3}$
$∴ \frac{d V}{d r} =$ Rate of change of volume of the sphere with respect to radius
$\frac{d V}{d r} = \frac{4}{3} π (3 r)^{2}$
$= \frac{4}{3} π (r)^{2}$
${(\frac{d V}{d r})}_{r = 7} = 4 π (7)^{2}$
$= 49 \times 4 \cdot π$
$= 196 π (c m)^{3} / c m$ .

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