Question

If the error in the radius of a circle is $0.2$ then the relative error in its area is

• A. $0.2$
• B. $0.1$
• C. $0.4$
• D. $0.3$

Answer 1

The correct option is A $0.2$

We know, area of circle $\left(A\right)$ is related to its radius $\left(r\right)$ as $-----$

$A=\pi r^2$

Or, $\log A=\log \pi +2\log r$

Differentials be taken,

Or, $dA=\frac{2}{\pi }\times \frac{2}{10}\times \frac{\pi r^2}{2r}=0.2$