question_answer

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions\[20\text{ }m\text{ }\times \text{ }16\text{ }m\]. Then, the area of the field in which the cow can graze is

A) \[154{{m}^{2}}\]

B) \[196{{m}^{2}}\]

C) \[228{{m}^{2}}\]

D) \[144{{m}^{2}}\]

Correct Answer: A

Solution :

Let ABCD be a rectangular field of dimensions \[20m\times 16\,m\]. Suppose, a cow is tied at a point A. Let length of rope be AE =14 m = r (say). \[\therefore \]Area of the field in which the cow graze = Area of sector AFEG \[=\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}\] \[=\frac{90{}^\circ }{360{}^\circ }\times \pi \times {{\left( 14 \right)}^{2}}\] [so, the angle between two adjacent sides of a rectangle is\[90{}^\circ \]] \[=\frac{1}{4}\times \frac{22}{7}\times 196=154{{m}^{2}}\]