Question

A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) = 0.)

Answer 1

Since a sphere's surface area is 4πr², we then need to find r as a function of time t, which is 9t (since it increases by 9 every second)+0 (the initial value)=9t. Plugging it in, we get 4π(9t)²=4π*36t²=144πt²