Question

An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long? 

Options

• 75 cm³/sec

• 750 cm³/sec

• 7500 cm³/sec

• 1250 cm³/sec

Answer 1

750 cm³/sec

Explanation:

Let x be edge of cube.

Given `dx/dt` = 10 cm/sec

Volume of the cube V = x³

∴ `(dV)/dt = 3x^2 dx/dt`

When x = 5 cm

`(dV)/dt` = 3 × 5² × 10

= 750 cm³/sec.