Question

The length and breadth of a field are measured as : l = (120 $\pm$ 2)m, b=(100 $\pm$ 5) m. What is the absolute error in the area of the field?

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is B

Now $\frac{△A}{A}=\frac{△l}{l}+\frac{△b}{b}=(\frac{2}{120}+\frac{5}{100})$ = 0.0667; $△A$ = 0.0667 x A

Now A = lxb = 120 $\times$ 100 = 12000$m^2$ $\Rightarrow △A$ = 0.0667 $\times$ 12000 = 800.4 $m^2$

(rounding off to 1 significant figures so 800$m^2$)

Area to the field = $A\pm △A$ = 12000 $\pm$ 800 = (1.2 $\times$ 0.08) $\times {10}^4{m}^2$