Question

The side of a cube is increasing at a rate of 2 kilometers per hour. At a certain instant, the side is 1.5. What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?

Answer 1

dV/dt = 13,5 [Km³/h]

Explanation:

The volume f the cube is:

V = x³ where x is a side of the cube, then tacking derivatives with respect to time on both sides of the equation

dV/dt = 3*x² dx/dt

dx/dt = 2 km/h

at the time when the side x = 1,5 Km

dV/dt = 3* (1,5)²*2 [km³/h]

dV/dt = 13,5 [Km³/h]