Question

a balloon which is always remains sperical on inflation is being infected by pumping in 900 cm cube per second find the rate at which the radius of the balloon increases when the radius is 15 CM

Answer 1

Answer is 1/π cm per second

w.k.t for sphere,
$v = \frac{4}{3} \pi {r}^{3}$
$\frac{dv}{dt} = 4\pi {r}^{2} \frac{dr}{dt}$
$900 = 4\pi \times 225 \times \frac{dr}{dt}$
$\frac{dr}{dt} = \frac{1}{\pi}$