A) Rs. 650
B) Rs. 355
C) Rs. 460
D) Rs. 264
Correct Answer: D
Solution :
| [d] Let the radius of a circular playground be r. |
| Given, Area of circular play ground |
| \[=22176\,c{{m}^{2}}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\pi {{r}^{2}}=22176\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{22}{7}{{r}^{2}}=22176\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}^{2}}=\frac{22176\times 7}{22}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}^{2}}=1008\times 7={{(12\times 7)}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,r=84\,cm\] |
| Now, circumference of play ground \[=2\pi r\] |
| \[=2\times \frac{22}{7}\times 84\] |
| \[=44\times 12=528\,cm\] |
| \[=\frac{528}{100}\,m\] \[[1\,m=100cm]\] |
| Cost of fencing of 1 meter ground \[=Rs.50\] |
| \[\therefore \] Cost of fencing of \[\frac{528}{100}\]metre ground |
| \[=Rs.\frac{528}{100}\times 50=Rs.264\] |
| Hence, required cost of fencing this ground is \[Rs.264\]. |
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