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

Options

A. `164 pm 3 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

A

Explanation

Given, length l = `(16.2 pm 0.1) cm`
Breadth b=`(10.1 pm 0.1)`
Area ` a= l xx b`
`=(16.2 cm) xx (10.1 cm) = 163.62 cm^2 `
Rounding off to three significant digits, area `A= 164 cm^2`
`(DeltaA)/(A) = (Deltal)/l = (Deltab)/b = (0.1)/(16.2) +(0.1)/(10.1)`
`=(1.01 + 1.62)/(16.2xx10.1) =(2.63)/(163.62)`
`implies DeltaA = A xx (2.63)/(163.62) = 163.22 xx (2.63)/(163.62) = 2.63cm^2`
`Delta A = 3cm^2` (By rounding off to one significant figure)
`therefore ` Area, `A= A pm DeltaA =(164 pm 3) cm^2`