Question

Air is being pumped into a spherical ballon at a rate of 10cm^3/min. Determine the rate at which the radius of the ballon is increasing when the radius of the ballon is 20cm

Answer 1

The volume of the ball is calculated by the formula $V=\frac {4\pi r^{3}} {3}$

The rate of change of volume is $\dot{V}=4\pi r^2 \dot{r}$

Thus, $\dot{r}=\frac{\dot{V} }{4\pi r^2}=(10 cm^3/min)/(4\pi (20cm)^2)=$ 0.00198943678864869169711104704216 cm/min