a spherical balloon is being inflated. Find the rate of change of the surface area of the balloon with respect to the radius when the radius is 10cm.

Question

A spherical balloon is being inflated. Find the rate of change of the surface area of the balloon with respect to the radius when the radius is 10cm.

Answer 1

The surface area of a sphere is related to the radius by the equation A(r)=4πr². Since you want the rate of change with respect to the radius, just take the derivative of this formula and you get A'(r)=8πr. Then plug 10cm in for r and you will have your answer.