Question

Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?

Answer 1

\[\text { Volume of the cube,} V = x^3 \]

\[\text { We have }\]

\[ ∆ x = 0 . 01x\]

\[\frac{dV}{dx} = 3 x^2 \]

\[ \Rightarrow ∆ V = dV = \frac{dV}{dx}dx = 3 x^2 \times 0 . 01x = 0 . 03 x^3 \]

\[\text { Hence, the approximate change in the value V of the cube is } 0 . 03 x^3 m^3 . \]

\[\text{Disclaimer: This solution has been created according to the question given in the book . However, the solution in the book is incorrect } . \]