Question

A cube is expanding in such a way that its edge is changing at a rate of 5cm/sec. If its edge is 4 cm. long, then the rate of change of its volume is

Answer 1

The rate of change of its volume is 240cm³/s.

Let us consider the edge length of the cube to be x cm.

So, the volume (V) of a cube with edge length x cm is x³ cm³

V = x³

Differentiating V with respect to time, we get:

dV/dt = 3x² dx/dt                             [d(xⁿ)/dt = nxⁿ⁻¹]

Given this dx/dt = Rate of change of edge length = 5cm/s, and edge length x = 4cm. Putting these values, we get

So, dV/dt = 3(4)²(5) = 240 cm³/s.

This is the rate of change of volume.