The volume of a spherical tank with radius = r is expanding in such a way that r is increasing at 1 cm/min. At what rate is the volume expanding when r = 100 cm?

Given that rate of expansion of radius is 1cm/min, that means
$$\frac{dr}{dt}=+1 \;cm/min$$
We know that volume of spherical tank would be given by
$$V=\frac43\pi r^3$$
Differentiate it both sides with respect to time to get rate of volume and using chain rule 
$$\frac{dV}{dt}=\frac43\pi (3r^2) \frac{dr}{dt}=4\pi  r^2 \frac{dr}{dt}$$
So when r is 100 cm we get, rate of volume as 
$$\frac{dV}{dt}=4\pi (100)^2 (1)= 40000\pi\; cm^3/min$$