Question

What will be the approximate change in the surface area of a cube of side xm caused by increasing the side by 2%.

(a) 0.24x

(b) 2.4x^2

(c) 0.4x^2

(d) 0.24x^2

I got this question in a national level competition.

I'm obligated to ask this question of Derivatives Application topic in division Application of Derivatives of Mathematics – Class 12

Answer 1

The correct option is (d) 0.24x^2

Easy explanation: Let the edge of the cube be x. Given that dx or Δx is equal to 0.02x(2%).

The surface area of the cube is A=6x^2

Differentiating w.r.t x, we get

\(\frac{dA}{dx}\)=12x

dA=(\(\frac{dA}{dx}\))Δx=12x(0.02x)=0.24x^2

Hence, the approximate change in volume is 0.24x^2.