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the radius of...

Question

the radius of a sphere increases at a rate of 2cm/sec. Find the rate at which its volume and area increases when radius is 4cm.

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Solution

$\frac{d r}{d t} = 2 c m / s e c$
Volume (V) = $\frac{4}{3} π r^{3}$
$\frac{d V}{d t} = 4 π r^{2} \frac{d r}{d t}$
$= 4 \times \frac{22}{7} \times 16 \times 2$ = $402.28$ $c m^{3} / s e c$
Area(A) = $π r^{2}$
$\frac{d A}{d t} = 2 π r \frac{d r}{d t}$
$= 2 \times \frac{22}{7} \times 4 \times 2$ = $50.28$ $c m^{2} / s e c$

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