Question

The circumference of a circle is measured as $56$ cm with an error $0.02$ cm. The percentage error in its area is

• A. $\frac{1}{7}$
• B. $\frac{1}{28}$
• C. $\frac{1}{14}$
• D. $\frac{1}{56}$

Answer 1

The correct option is C $\frac{1}{14}$

Circumference of circle $C=2\pi r=56cm$

$\Rightarrow r=\frac{28}{\pi }$

Also, $\frac{dC}{dr}=2\pi$

Area of circle $A=\pi r^2$

$\frac{dA}{dr}=2\pi r$

$\Rightarrow \frac{dA}{dC}=r=\frac{28}{\pi }$

Approximate error in A $=dA=\left(\frac{dA}{dC}\right)\Delta C$

$=r\left(0.02\right)$

$\Rightarrow \frac{dA}{A}=\frac{0.02}{\pi r}=\frac{1}{1400}$

Percentage error in A is $\frac{1}{14}$%