A spherical balloon is being inflated at a rate of 27π in³/sec

How fast is the radius of the balloon increasing when the radius is 3 in?

dV/dt = 27pi in^3/sec

V = (4/3) * pi * r^3
dV/dt = 3 * (4/3) * pi * r^2 * dr/dt
dV/dt = 4 * pi * r^2 * dr/dt

r = 3
dV/dt = 27 * pi

27 * pi = 4 * pi * 3^2 * dr/dt
27 = 4 * 9 * dr/dt
3/4 = dr/dt

The radius is increasing at 3/4 inches per second

dV/dt = 27π in³/sec = 4πr²(dr/dt)

dr/dt when r = 3: (27π in³/sec) * 1/(36π in²) = 3/4 in/sec