question_answer

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)   \[(55.4\pm 0.26)c{{m}^{2}}\] Surface area, \[S=4\pi {{r}^{2}}=4\times \frac{22}{7}\times {{(2.1)}^{2}}=55.44=55.4\,\,c{{m}^{2}}\] Further,               \[\frac{\Delta S}{S}=2\cdot \frac{\Delta r}{r}\] or                            \[\Delta S=2\left( \frac{\Delta r}{r} \right)(S)\]         \[=\frac{2\times 0.5\times 55.4}{2.1}=26.38=26.4\,\,c{{m}^{2}}\] \[\therefore \]                    \[S=(55.4\pm 26.4)c{{m}^{2}}\]