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 ______.

पर्याय

• 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 `underline(164 ± 3 cm^2)`.

Explanation:

Given, Length `l = (16.2 +- 0.1)` cm

Breadth `b = (10.1 +- 0.1)` cm

Area = `A = l xx b`

= (16.2 cm) × (10.1 cm) 

= 163.62 cm²

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

`(ΔA)/A = (Δl)/l + (Δb)/b = 0.1/16.2 + 0.1/10.1`

= `(1.01 + 1.62)/(16.2 xx 10.1)`

= `2.63/163.62`

⇒ `ΔA = A xx 2.63/163.62`

= `163.62 xx 2.63/163.62`

= 2.63 cm²

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

∴  Area, A = A ± ΔA = (164 ± 3) cm².