question_answer

Semi-circular lawns are attached to the edges of a rectangular field measuring\[42\,\,m\times 35\,\,m\]. Find the area of the total field.

A) \[3895.6\,\,{{m}^{2}}\]       

B)  \[3818.5\,\,{{m}^{2}}\]

C) \[3735.6\,\,{{m}^{2}}\]                   

D)  \[3899.9\,\,{{m}^{2}}\]

Correct Answer: B

Solution :

From figure, it is seen that total area of lawn on length face = circle \[{{C}_{1}}=\pi {{l}^{2}}/4\] \['l'\] becomes diameter. Similarly, \[{{C}_{2}}=\frac{\pi {{b}^{2}}}{4}\] \[\therefore \]  Total area \[=\frac{\pi }{4}\times \left( {{42}^{2}}+{{35}^{2}} \right)\] \[=\frac{11\times 7}{2}\left( {{6}^{2}}+{{5}^{2}} \right)\frac{77\times 61}{2}\] To, this we add are of rectangle, \[{{A}_{2}}=l\times b\] \[=42\times 35=1470\Rightarrow \]Total area \[=\frac{77\times 61}{2}+1470\]