Question

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

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

Answer 1

Answer: (A)

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