If the solve the problem


If $V=\frac{4}{3} \pi r^{3}$, at what rate in cubic units is $V$ increasing when $r=10$ and $\frac{d r}{d t}=0.01 ?$

(a) $\Pi$

(b) $4 \pi$

(c) $40 \pi$

(d) $4 \pi / 3$


(b) $4 \pi$

Given: $V=\frac{4}{3} \pi r^{3}, r=10$ and $\frac{d r}{d t}=0.01$

$\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$

$\Rightarrow \frac{d V}{d t}=4 \pi(10)^{2} \times 0.01$

$\Rightarrow \frac{d V}{d t}=4 \pi$

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