Question

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

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

Answer 1

Answer: (C)

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