Question

In measuring the circumference $100$cm of a circle, there is an error of $0.05$cm then percentage error in its area is?

• A. $\frac{1}{10}$
• B. $\frac{1}{5}$
• C. $\frac{1}{100}$
• D. $1$

Answer 1

The correct option is A $\frac{1}{10}$

Circumference $\left(P\right)=100cm\pm 0.05cm$

$\because p=2\pi r$

$\because dp=2\pi dr$

$\Rightarrow dr=\frac{0.05}{2\pi }$

$\because A=\pi r^2$

$\Rightarrow dA=2\pi rdr$

$=p.dr$

$=100\times \frac{0.05}{2\pi }$

$=0.8$

$\therefore$ percentage error in area $=\frac{dA}{A}\times 100$

$=\frac{100\times \frac{0.05}{2\pi }}{\pi \times {\left(\frac{100}{2\pi }\right)}^2}$

$=\frac{0.05\times 2}{100}\times 100$

$=\frac{1}{10}$