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?

Question

Philoid · Accepted Answer

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

V = x³

…….. by chain rule

It is given that

Then,

Thus, when x = 10cm

Then

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