Find the approximate change in the volume `V` of a cube of side `x` meters caused by increasing the side by 2%.

Explanation

Given that side of a cube is `x` meters

so, the volume of a cube will be `V=x^3`

Now,
the side `x` is increased by `2%`
so the new length of side will be
`x(1+2/100)=(51x)/50`

The new volume will be
`V_1=((51x)/50)^3=(51/50)^3 x^3`

Therefore, the change in volume is
` V_1−V=((51/50)^3−1)x^3`

The percentage change in volume is :
`=(V_1−V)/V×100`

`=((51/50)^3−1)/1×100`

`=(51^3−50^3)/50^3×100`

...