question_answer

A horse is tethered to a peg with a 14-metre-long rope at the corner ofa40-m-long and 20m-wide rectangular grass-field. What area of field does the horse graze?

A) \[150{{m}^{2}}\]                    

B) \[154{{m}^{2}}\]        

C)        \[167{{m}^{2}}\]        

D)        \[171{{m}^{2}}\]

E) \[161{{m}^{2}}\]

Correct Answer: B

Solution :

As the horse is pegged at the comer of the rectangular field, it will graze the area of the field enclosed between the sides of the rectangle and the arc. Area of the field\[=\frac{1}{4}\pi {{r}^{2}}=\frac{1}{4}\times \frac{22}{7}\times 14\times 14\] \[=154\,\,{{m}^{2}}\]