Question

A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi or 12.56637061 square centimeters?

Answer 1

Volume = V = (4/3) pi r^3
dV/dt = 4 pi r^2 dr/dt
When the area 4 pi r^2 = 4 pi, the value of r is 1.

At that instant,
dV/dt = 4 pi *(1 cm^2)*2 cm/s
= 8 pi cm^3/s

Answer 2

A. Spherical balloon filled with helium at 1 atm just lift a 2kg lead what is its radius