Question

A plate has a length $\left(5 \pm 0.1\right) \, cm$ and breadth $\left(2 \pm 0.01\right) \, cm.$ Then the area of the plate is

• A. $\left(10 \, \pm 0.25\right) \, cm^{2}$
• B. $\left(10 \, \pm 0.01\right) \, cm^{2}$
• C. $\left(10 \, \pm 0.001\right) \, cm^{2}$
• D. $\left(10 \, \pm 1\right) \, cm^{2}$

Answer 1

Answer: (A)

$\text{A} = \text{ab}$
$\frac{\Delta \text{A}}{\text{A}} = \frac{\Delta \text{a}}{\text{a}} + \frac{\Delta \text{b}}{\text{b}}$
$= \frac{\text{0.1}}{\text{5}} + \frac{\text{0.01}}{2}$
$=\frac{\text{0.2+0.05}}{1 0}$
$=\frac{0 . 25}{10}$
$\Delta \text{A}=\text{0.025}\times \text{A}$
$=\text{0.25}cm^{2}$