Question

A spherical balloon is inflated with gas at the rate of 600 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 30 centimeters? ( Vsphere = 4pi/3 * radius^3)

Answer 1

Considering the ballon to be spherical
It's volume is given by 4/3(π r^3) by differentiating volume with respect to time we get rate of change of volume hence,
4πr^2(dr/dt)=600÷60=10
Substituting r=30cm
4π(30)*(30)(dr/dt)=10
dr/dt=rate of increase in bullion's radius=1/(360π)cm/s