question_answer

Four cows are tied at the four corner of the square field of side 35 m, so that they can just reach to each other. What is the area of the field which remain ungreased?

A) \[256.7\text{ }c{{m}^{2}}\]          

B)   \[262.5\text{ }c{{m}^{2}}\]

C) \[555.5\text{ }c{{m}^{2}}\]                 

D) \[985.6\text{ }c{{m}^{2}}\]

E) None of these

Correct Answer: B

Solution :

Explanation Clearly, the shaded portion of the square shows the area of the field remain ungrazed. Radius of each of the circle \[=\,\,\,\frac{35 }{2} = 17.5 cm\] Area grazed by 1 cow \[=\,\,\frac{\pi {{r}^{2}}\theta }{360} = \frac{22}{7} \times  17.5 \times  17.5\times 90\times \frac{1}{360}=240.625\,c{{m}^{2}}\]Area grazed by four cows \[= 4 \times  240.625 c{{m}^{2}}= 962.5 c{{m}^{2}}\] Area of field remain ungrazed = Area of field -Area of grazed region \[=\,\,\,1225-962.5 =262.5 c{{m}^{2}}.\]