Question

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 8 cm?

Answer 1

A = surface area = (4/3) pi r^2
so
d A/dt = (8/3) pi r dr/dt

now get dr/dt from:

D Volume = surface area*dr=(4/3) pi r^2 dr
so
dV/dt = (4/3)pi r^2 dr/dt