question_answer

Semi circular lawns are attached to the edges of a rectangular field measuring\[42\text{ }m\times 35\text{ }m\]. 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 :

(b): 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,\[{{A}_{2}}=1\times b\] \[=42\times 35=1470\Rightarrow \]Total area \[=\frac{77\times 61}{2}1470\]