Question

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

• A. $(55.4 \pm 26.4) cm ^{2}$
• B. $(55.4 \pm 0.02) cm ^{2}$
• C. $(55.4 \pm 2.64) cm ^{2}$
• D. $(55.4 \pm 0.26) cm ^{2}$

Answer 1

Answer: (A)

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