A) \[12\text{ }c{{m}^{2}}\]
B) \[13\,c{{m}^{2}}\]
C) \[14\,c{{m}^{2}}\]
D) None of these
Correct Answer: D
Solution :
| Given, perimeter of a protractor = 72 cm |
| \[\therefore \,\,\,\pi r+2r=72\] [\[\because\] perimeter of a protractor = perimeter of semi-circle] |
| where, r is the radius of circle. |
| \[\Rightarrow \,\,\,r\left( \frac{22}{7}+2 \right)=72\Rightarrow r\times \frac{36}{7}=72\] |
| \[\Rightarrow \,\,\,r=2\times 7\Rightarrow \,r=14\,cm\] |
| \[\therefore\] Area of protractor \[=\frac{\pi {{r}^{2}}}{2}=\frac{22}{7}\times \frac{{{\left( 14 \right)}^{2}}}{2}\] |
| \[=\text{ }308\text{ }c{{m}^{2}}\] |
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