A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) Find the rate of change of the radius (in cm/min) when r = 50 centimeters and r = 75 centimeters.

Answer 1

Answer 2

V = 4/3πr³; dV/dt = 4πr²dr/dt; dr/dt = dV/dt/(4πr²)

r = 50 cm, dr/dt = 500cm³/min/(4π·2500cm²) = 0.01592 cm/min;

r = 75 cm, dr/dt = 500cm³/min/(4π·5625cm²) = 0.00712 cm/min;