A spherical balloon expands uniformly as it is inflated. The radius of the balloon in r meters at time t seconds. Find the radius, the volume, and the surface area of the balloon when the rates of increase of the surface area of the balloon and the radius are numerically equal

Answer 1

da/dt = 8πr dr/dt
If da/dt = dr/dt, then r = 1/8π

so, now you can find the area and volume.

Answer 2

Steve, what is dr/dt? how did you get 1/8pi?