Question

The length and width of a rectangular room are measured to be $3.95 \pm 0.05\, m$ and $3.05 \pm 0.05\, m$, respectively. The area of the floor is

• A. $1205 \pm 0.01\, m^{2}$
• B. $12.05 \pm 0.005\, m^2$
• C. $1205 \pm 0.34\, m^2$
• D. $1205 \pm 0.40\, m^2$

Answer 1

Answer: (C)

Area, $A =l \times b$
$=3.95 \times 3.05=12.05\, m ^{2}$
Now, $A=l \times b$
$\Rightarrow \frac{d A}{A}=\frac{d l}{l}+\frac{d b}{b}$
$\Rightarrow \Delta A =\left(\frac{\Delta l}{l}+\frac{\Delta b}{b}\right) \times A$
$=\left(\frac{0.05}{3.95}+\frac{0.05}{3.05}\right) \times 12.05$
$\approx 0.34$
So, area of floor is $A=12.05 \pm 0.34\, m ^{2}$.