Question

The circumference of a circle is measured as $28cm$ with an error of $0.01cm$. The percentage error in the area is

• A. $\frac{1}{14}$
• B. $0.01$
• C. $\frac{1}{7}$
• D. none of these

Answer 1

Answer: (A)

$\frac{1}{14}$

Circumference $C=2\pi r$
$\Rightarrow r=\frac{14}{\pi }$
Also, $\frac{dC}{dr}=2\pi$
Area of circle $A=\pi r^2$
$\Rightarrow A=\frac{{14}^2}{\pi }$
Also, $\frac{dA}{dr}=2\pi r$
$\Rightarrow \frac{dA}{dC}=r=\frac{14}{pi}$
Approximate error in $A$ is $dA=\left(\frac{dA}{dC}\right)\Delta C$
$=\frac{14}{\pi }\frac{1}{100}$
$=\frac{1}{1400}$ of A
Percentage error in $A=\frac{1}{14}\%$