Question

A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is V(r)= 4/3 πr^3 and the surface area of a sphere in terms of its radius is S(r)= 4πr^2, estimate the rate
at which the volume of the balloon is changing with respect to its surface area when the surface area
measures 50cm cubed.

Answer 1

dV/dt = 4πr^2 dr/dt
dS/dt = 8πr dr/dt

dV/dS = (dV/dt) / (dS/dt) = r/2
So now just find r when A = 50