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Question
Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1% ?
Solution
Let y be the surface area of the cube.
\[y = 6 x^2 \]
\[\text { We have }\]
\[ \frac{\bigtriangleup x}{x} \times 100 = 1\]
\[\text { Now }, \]
\[\frac{dy}{dx} = 12x\]
\[ \Rightarrow \bigtriangleup y = dy = \frac{dy}{dx}dx = 12x \times \frac{x}{100} = 0 . 12 x^2 m^2 \]
\[\text { Hence, approximate change in the surface area of the cube is }0 . 12 x^2 m^2 .\]
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