Question

If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?

Answer 1

Let x be the radius and y be the area of the circular plane.

\[\text { We have } \frac{\bigtriangleup x}{x} = \alpha \text { and } y = x^2 . \]

\[ \Rightarrow \frac{dy}{dx} = 2x\]

\[ \Rightarrow \frac{\bigtriangleup y}{y} = \frac{2x}{y}dx = \frac{2x}{x^2} \times \alpha x = 2\alpha\]

\[\text { Hence, the relative error in the area of the circular plane is } 2\alpha .\]