| The circumference of two circles is 88 m and 220 m, respectively. What is the difference between the area of the larger circle and the smaller circle? |
A) \[3422\,\,{{m}^{2}}\]
B) \[3242\,\,{{m}^{2}}\]
C) \[3234\,\,{{m}^{2}}\]
D) \[3424\,\,{{m}^{2}}\]
E) None of these
Correct Answer: C
Solution :
| Given, \[2\pi {{r}_{1}}=88\]\[\Rightarrow \]\[{{r}_{1}}=\frac{88\times 7}{2\times 22}=14\] |
| and \[2\pi {{r}_{2}}=220\]\[\Rightarrow \]\[{{r}_{2}}=\frac{220\times 7}{2\times 22}=35\] |
| \[\therefore \]\[\pi (r_{2}^{2}-r_{1}^{2})=\frac{22}{7}\,\,({{35}^{2}}-{{14}^{2}})\] |
| \[=\frac{22}{7}\,\,(1225-196)\] |
| \[=\frac{22}{7}\times 1029=3234\] |
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