Question

The length of a side of a square field is 20 mtr. A cow is tied at the corner by means of a 7 mtr long rope. Find the area of the field which cow can graze. If the length of rope is doubled then find the increase in the grazing area.

Answer 1

Let ABCD represents the square field having each side of 20 mtr.
Let the cow is tied at point A by means of a 7 mtr long rope.
So the cow can move and gaze in the circular area having radius 7 mtr.
The maximum area that a cow can gaze is
$=\frac{1}{4}\pi r^2$
$=\frac{1}{4}\times \frac{22}{7}\times (7{)}^2$
$=38.5sq.mtr$
$\therefore$ The cow can gaze 38.5 sq. mtr are of the field.
If the length of the rope is doubled then r = 14 mtr.
The maximum area that a cow can gaze is
$=\frac{1}{4}\pi r^2$
$=\frac{1}{4}\times \frac{22}{7}\times (14{)}^2$
$=154sq.mtr.$
Increase in the gazing area = 154 - 38.5 = 115.5 sq. mtr
Increase in the gazing area is 115.5 sq. mtr.