The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 6 in. long and increasing at the rate of 0.3 in./sec. How fast is the volume of the cube changing at that instant of time?

Answer 1

V = x^3
dV/dt = 3x^2 dx/dt

given: when x = 6 , dx/dt = .3

dV/dt = 3(36)(.3) = 32.4 cubic inches/sec