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 +- 3 cm^(2)`
B. `163.62 +- 2.6 cm^(2)`
C. `163 +- 2.6 cm^(2)`
D. `163.62 +- 3 cm^(2)`

Answer

a

Explanation

If `Delta x` iws error in a physical quantity then releative error is calculate as`(Delta x)/(x)` given , length
`1 = (16.2 +- 0.1)cm`
Breadth `b = (10.1 +- 0.1)cm`
Area `A = 1 xx b = 16.2 xx 10.1 = 163.62cm^(2)`
Rounding off to three significant digth area `A = 164 cm^(2)`
`(Delta A)/(A) = (Delta I)/(I)+(Delta b)/(b) = (0.1)/(16.2) + (0.1)/(10.1)`
`= (1.01 + 1.62)/(16.2 xx 10.1) = (2.63)/(163.62)`
`rArr Delta A = A xx (2.63)/(163.62)`
`= 163.62 xx (2.63)/(163.62) = 2.63 cm^(2)`
`Delta A = 3 cm^(3)` (by rounding off to one significant figure) Area `A = A +- Delta A = (164 =3)cm^(2)`.