Answer
a) 0.0707 cm/min
b) 0.0177 cm/min
Work Step by Step
The volume of a sphere is $\frac{4}{3} \pi r^3 $
The change in volume is given by $\frac {dV}{dt} = (4/3) (3) \pi r^2 = 4 \pi r^2 \frac{dr}{dt} $
We are told the volume is changing at a rate of + 800 $cm^3$ (positive since inflated)
$800 = 4 \pi r^2 {dr}{dt} $
a) when the radius is 30cm, we solve for dr/dt
$\frac {dr}{dt} = 0.0707 cm/min $
b) when the radius is 60cm, we solve for dr/dt
$\frac {dr}{dt} = 0.0177 cm/min $
