Question

The radius of sphere is measured to be $(2.1\pm 0.5)$cm.
Calculate its surface area with error limits.

• A. $S=(55.4\pm 26.4)c{m}^2$
• B. $S=(55.4\pm 26.4)m{m}^2$
• C. $S=(55.4\pm 13.2)c{m}^2$
• D. None of these

Answer 1

The correct option is A $S=(55.4\pm 26.4)c{m}^2$

Surface area, $S=4\pi r^2=\left(4\right)\left(\frac{22}{7}\right){\left(2.1\right)}^2$$=55.44=55.4c{m}^2$
Further, $\frac{\Delta S}{S}=2.\frac{\Delta r}{r}$
$\Delta S=2\left(\frac{\Delta r}{r}\right)\left(S\right)=\frac{2\times 0.5\times 55.4}{2.1}$$=26.38=26.4c{m}^2$

$\therefore S=(55.4\pm 26.4)c{m}^2$