Question

air is being pumped into a spherical balloon at a rate of 5cm^3/min. Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 20 cm

Answer 1

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

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

$\frac{dr}{dt}=\frac{1}{4\pi r^2}\frac{dV}{dt}$

When $\frac{dV}{dt}=5\;\frac{cm^3}{min},\;r=20cm:$

$\frac{dr}{dt}=\frac{1}{320\pi}\approx 0.001\frac{cm}{min}$