Question

The edge of a variable cube is increasing at the rate of 10 cm/sec. How fast is the volume of the cube increasing when the edge is 5 cm long?

Answer 1

Let the edge of a cube be x units.

∴ `dx/dt` = 10 cm/sec   ...[Given]

Now, Volume of cube (V) = x³

Differentiating w.r.t. t, we get

`(dV)/dt = 3x^2 dx/dt`

⇒ `(dV)/dt = 3 xx 5^2 xx 10`   ...[∵ x = 5 cm]

⇒  `(dV)/dt = 750`

Hence, the volume of the cube is increasing at the rate of 750 cm³/sec.