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) \[(55.4\,\pm \,0.26)\,c{{m}^{2}}\]
Correct Answer: A
Solution :
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 \[\Delta S=2\left( \frac{\Delta r}{r} \right)(S)\] \[=\frac{2\times 0.5\times 55.4}{2.1}=26.38=26.4\,c{{m}^{2}}\] \[\therefore \] \[S=(55.4\,\pm \,26.4)c{{m}^{2}}\]
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