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.

Answer 1

$\frac{dr}{dt}=2cm/sec$

Volume (V) = $\frac{4}{3}\pi r^3$

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

$=4\times \frac{22}{7}\times 16\times 2$ = $402.28$ $c{m}^3/sec$

Area(A) = $\pi r^2$

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

$=2\times \frac{22}{7}\times 4\times 2$ = $50.28$ $c{m}^2/sec$