Question

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 40 mm?

Answer 1

V = 4/3*Pi*R^3
dV/dt = 4/3 * Pi * 3*R^2*dR/dt
dV/dt = 4*Pi*R^2*dR/dt

when diameter is 40 , Radius = 20. and dR/dt = 4. (make sure units are consistent)

dV/dt = 4*Pi*(20)^2 * 4

Answer 2

Thank you!

Answer 3

hmm..