| A playground is in the form of a rectangle having semicircles on the shorter sides, its area, when the length of the rectangular portion is \[\text{7}0\text{ m}\] and the breadth is \[\text{56 m},\] is: |
 |
A) \[6274\,{{m}^{2}}\]
B) \[7476\,{{m}^{2}}\]
C) \[6384\,{{m}^{2}}\]
D) \[7274\,{{m}^{2}}\]
Correct Answer: C
Solution :
| [c] We have. length of rectangle \[(l)=70m\]and breadth of rectangle \[(b)=56m\] |
| Radius of circle \[(r)=\frac{56}{2}=28m\] |
| Area of the field |
| = area of the rectangle + Area of the semicircular ends on the shorter sides \[\therefore \] Area of the field \[=l\times b+2\times \frac{\pi }{2}{{r}^{2}}\] |
| \[=(70\times 56)+\left( 2\times \frac{22}{2}\times \frac{28\times 28}{7} \right)\] |
| \[=3920+2464=6384{{m}^{2}}\] |
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