Question

9. The approximate change in the volume of a cube of side x metres caused byincreasing the side by 3% is(A) 0.06x3m* (B) 0.6x3 m3 (C) 0.09 x3 m3 (D) 0.9x3m3

Answer 1

Given, side of cube is x m and side increases by 3%.

Volume of a cube with side x is,

V= x 3

The approximate change in volume is,

ΔV= dV dx Δx = d( x 3 ) dx Δx =3 x 2 Δx

Side increases by 3%, hence Δx=0.03x.

Substitute the value Δx=0.03xin the above equation, we get

ΔV=3 x 2 ×0.03x =0.09 x 3   m 3

The approximate change in volume is 0.09 x 3   m 3 .

Thus, option (C) is correct.