A) \[2310\,{{m}^{2}}\]
B) \[1513\,{{m}^{2}}\]
C) \[1920\,{{m}^{2}}\]
D) \[2854\,{{m}^{2}}\]
Correct Answer: A
Solution :
| [a] Let radii of inner and outer sides are \[{{r}_{1}}\] and \[{{r}_{2}}\]. |
| Width of road \[(d)=7m\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,{{r}_{2}}={{r}_{1}}+d=({{r}_{1}}+7)\,m\] |
| Given, Circumference of outer side \[=352\,m\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\pi {{r}_{2}}=352\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\times \frac{22}{7}\times {{r}_{2}}=352\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{2}}=56\,m\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{1}}=56-7=49\,m\] |
| So, required area of road \[=\pi (r_{2}^{2}-r_{1}^{2})\] |
| \[=\frac{22}{7}({{r}_{2}}-{{r}_{1}})\,\,\,\,({{r}_{2}}+{{r}_{1}})\] |
| \[=\frac{22}{7}(56-49)\,\,\,\,(56+49)\] |
| \[=\frac{22}{7}\times 7\times 105=2310\,{{m}^{2}}\] |
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