Question

Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.

Answer 1

The formula for volume of a cube V of side x m is given by,

V= x 3 (1)

Let, Δx be the approximate change in x , then, for very small change in volume dV we have,

dV=( dV dx )Δx(2)

Differentiate the equation (1) with respect to x.

dV dx =3 x 2

It is given that increase in side is 1%. So, the change in side x is,

Δx= 1 100 x =0.01x

Substitute the values in the above expression.

dV=3 x 2 ( 0.01x ) =0.03 x 3

Thus, the approximate change in volume V of cube with side x m is 0.03 x 3   m 3 .