Question

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

• A. $164\pm3 \,cm^{2}$
• B. $163.62 \pm 2.6 \, cm^{2}$
• C. $163.6 \pm 2.6 \,cm^{2}$
• D. $163.62 \pm 3 \,cm^{2}$

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 $l=\left(16.2\pm0.1\right)\,cm$
Breadth $b=\left(10.1\pm0.1\right)\,cm$
Area $A=l\times b=16.2\times10.1=163.62\,cm^{2}$
Rounding off to three significant digits, area $A=164\,cm^{2}$
$\frac{\Delta A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b}=\frac{0.1}{16.2}+\frac{0.1}{10.1}$
$=\frac{1.01+1.62}{16.2\times10.1}=\frac{2.63}{163.62}$
$\Rightarrow \Delta A=A\times\frac{2.63}{163.62}$
$=163.62\times\frac{2.63}{163.62}=2.63\,cm^{2}$
$\Delta A=3 \,cm^{2}$(By rounding off to one significant figure)
Area, $A=A\pm\Delta A=\left(164\pm3\right)\,cm^{2}$