Question

All edges of a cube are expanding at a rate of 6 cm/sec. How fast is the volume changing when each edge is (a) 2 cm and (b) 10 cm?

Answer 1

As volume is cube of the length:

V(e) = e^3

So the rate of change of the volume is or differentiating :

dV/dt = dV/de * de/dt = 3e^2 de/dt = 12 e^2 cm/sec

when each edge is 5 cm, dV/dt = 12 * 25 = 300 cm^3/sec
When each edge is 12cm, dV/dt = 12 * 12^2 = 1728 cm^3/sec