Question

The edge of a cube is increasing at the rate of 20 cm/sec. How fast is the volume of the cube increasing when the edge is 6 cm long?

Options

• 432 cm³/sec 

• 2160 cm³/sec 

• 180 cm³/sec

• 1920 cm³/sec

Answer 1

2160 cm³/sec 

Explanation:

`(da)/dt =  20` ............(i)

But if a is edge of a cube, then V = a³

∴ `(dV)/dt = 3a^2 (da)/dt = 3a^2 . 20`

`= 60a^2 = 60 xx (6)^2` ..........[∵ edge a = 6 cm]

= 2160 cm³/sec