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. `163.62pm 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)cm`
Area, `A=lxxb=(16.2xx10.1)cm^(2)`
`=163.62cm^(2)= 164cm^(2)` (3 significant figures)
Relative error in A is `(triangleA)/(A)=(triangle l)/(l)+(triangle b)/(b)`
`=(0.1)/(16.2)+(0.1)/(10.1)`
`=(6.173+9.901)xx10^(-3)`
`=16.074xx10^(-3)= 0.016074 = 0.016`
`triangleA= 0.016xxA`
`=0.016xx164cm^(2)`
`=2.636cm^(3)`
`=3 cm^(2)` (1 significant figures)
Area, `A=(164 pm 3)cm^(2)`.