Question

Find the approximate change in the volume of cube of side xm caused by increasing the side by 6%.

(a) 0.18x

(b) 0.18x^3

(c) 0.18x^2

(d) 1.8x^3

This question was addressed to me in unit test.

Enquiry is from Derivatives Application in division Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (b) 0.18x^3

For explanation I would say: We know that the volume V of a cube is given by

V=x^3

Differentiating w.r.t x, we get

\(\frac{dV}{dx}\)=3x^2

dV=(\(\frac{dV}{dx}\))Δx=3x^2 Δx

dV=3x^2 (6x/100)=0.18x^3

Therefore, the approximate change in volume is 0.18x^3.