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

The Correct Option is A

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}} $