Question

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Answer 1

Let x be the length of a side and V be the volume of the cube. Then,

V = x^3.

∴ (By chain rule)

It is given that,

∴

Thus, when x = 10 cm,

Hence, the volume of the cube is increasing at the rate of 900 cm³/s when the edge is 10 cm long.