| The circumference of two circles is 88 m and 220 m, respectively. What is the difference between the area of the larger circle and smaller circle? [Andhra Bank (PO) 2011] |
A) \[3422\,\,{{m}^{2}}\]
B) \[3244\,\,{{m}^{2}}\]
C) \[3242\,\,{{m}^{2}}\]
D) \[3234\,\,{{m}^{2}}\]
E) None of these
Correct Answer: D
Solution :
| \[2\pi {{r}_{1}}=88\]\[\Rightarrow \,\]\[{{r}_{1}}=\frac{88\times 7}{2\times 22}=14\,m\] |
| Area \[=\pi r_{1}^{2}=\frac{22}{7}\times 14\times 14=616\,{{m}^{2}}\] |
| Again, \[2\pi {{r}_{2}}=220\]\[\Rightarrow \,\]\[{{r}_{2}}=\frac{220\times 7}{2\times 22}=35\,m\] |
| Area \[\pi r_{2}^{2}=\frac{22}{7}\times 35\times 35=3850\,{{m}^{2}}\] |
| Difference \[=3850-616=3234\,{{m}^{2}}.\] |
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