Question

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm?.

Answer 1

V = 4/3 π R^3 = 4/3 π (D/2)^3 = 1/6 π D^3

dV / dD = 1/2 π D^2 rate of change of volume related to diameter

dV = 1/2 π D^2 dD

dV = 1/2 π 80^2 * 4 mm^3 the radius increases at 1/2 the speed of the diameter

dV = 40,200 mm^3/s