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)

$(55.4\,\pm \,26.4)\,c{{m}^{2}}$

Answer 2

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