Question

A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fast is the volume of the balloon increasing when the radius is 3 cm

Answer 1

72πcm³/s

Explanation:

Volume of the spherical balloon V = 4/3πr³

dV/dr = 4πr²

The rate at which the volume of the balloon increasing is expressed as;

dV/dt = dV/dr • dr/dt

dV/dt = 4πr² • (2)

Given

Radius r = 3cm

dV/dt = 4π(3)² • (2)

dV/dt = 36π×2

dV/dt = 72πcm³/s

Hence the rate at which the volume is increasing is 72πcm³/s