Question

Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?

Answer 1

Let y be the surface area of the cube.

\[y = 6 x^2 \]

\[\text { We have }\]

\[ \frac{\bigtriangleup x}{x} \times 100 = 1\]

\[\text { Now }, \]

\[\frac{dy}{dx} = 12x\]

\[ \Rightarrow \bigtriangleup y = dy = \frac{dy}{dx}dx = 12x \times \frac{x}{100} = 0 . 12 x^2 m^2 \]

\[\text { Hence, approximate change in the surface area of the cube is }0 . 12 x^2 m^2 .\]