Question

The length and breadth of a rectangular sheet are $16.2cm$ and $10.1cm,$ respectively. The area of the sheet in appropriate significant figures and error is

• A. $164\pm 3c{m}^2$
• B. $163.62\pm 2.6c{m}^2$
• C. $163.6\pm 2.6c{m}^2$
• D. $163.62\pm 3c{m}^2$

Answer 1

Answer: (A)

If $\Delta x$ is error in a physical quantity, then relative error is calculated as $\frac{\Delta x}{x}$

Given, length $l=\left(16.2\pm 0.1\right)cm$

Breadth $b=\left(10.1\pm 0.1\right)cm$

Area $A=l\times b=16.2\times 10.1=163.62c{m}^2$

Rounding off to three significant digits, area $A=164c{m}^2$

$\frac{\Delta A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b}=\frac{0.1}{16.2}+\frac{0.1}{10.1}$

$=\frac{1.01+1.62}{16.2\times 10.1}=\frac{2.63}{163.62}$

$\Rightarrow \Delta A=A\times \frac{2.63}{163.62}$

$=163.62\times \frac{2.63}{163.62}=2.63c{m}^2$

$\Delta A=3c{m}^2$(By rounding off to one significant figure)

Area, $A=A\pm \Delta A=\left(164\pm 3\right)c{m}^2$