Question

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

विकल्प

• 164 ± 3 cm²

• 163.62 ± 2.6 cm²

• 163.6 ± 2.6 cm²

• 163.62 ± 3 cm²

Answer 1

The length and breadth of a rectangular sheet are 16.2 cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is ${\displaystyle \underline{164\pm 3c{m}^2}}$.

Explanation:

Given, Length ${\displaystyle l=(16.2\pm 0.1)}$ cm

Breadth ${\displaystyle b=(10.1\pm 0.1)}$ cm

Area = ${\displaystyle A=l\times b}$

= (16.2 cm) × (10.1 cm) 

= 163.62 cm²

Rounding off to three significant digits, area A = 164 cm²

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

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

= ${\displaystyle \frac{2.63}{163.62}}$

⇒ ${\displaystyle \Delta A=A\times \frac{2.63}{163.62}}$

= ${\displaystyle 163.62\times \frac{2.63}{163.62}}$

= 2.63 cm²

ΔA = 3 cm²   .......(By rounding off to one significant figure)

∴  Area, A = A ± ΔA = (164 ± 3) cm².