Question

The circumference of a circle is measured as $268cm$ 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. $Noneofthese$

Answer 1

The correct option is

A

$\frac{1}{14}$

Let radius, circumference and area of the circle be r, C and A respectively.

$C=2\pi r$

$268=2\pi r$

$r=\frac{134}{\pi }$

$\delta C=2\pi \delta r$

$=0.01$

$\delta r=\frac{0.01}{2\pi }$

$A=\pi r^2$

$\delta A=2\pi r\delta r$

$\frac{\delta A}{A}=\frac{2\pi r\delta r}{\pi r^2}$

$=\frac{2\delta r}{r}$

$=\frac{\frac{2\times 0.01}{2\pi }}{\frac{134}{\pi }}$

$=\frac{0.01}{134}$

The percentage error in the area $=\frac{0.01}{134}\times 100$

$=\frac{1}{134}$