A horse is tied to a peg at one corner of a square shaped grass field of side $15\ m$ by means of a $5\ m$ long rope. Find the area of that part of the field in which the horse can graze.
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Given: A horse is tied to a peg at one corner of a square shaped grass field of side $15\ m$ by means of a $5\ m$ long rope.
To do: To find the area of that part of the field in which the horse can graze.
Solution:
As given in the question,
The maximum area can be grazed by the horse is the area of the quadrant of the circle with radius $r=5\ m$.
Therefore, Area grazed by the horse$=$ Area of the quadrant $( 5\ m)$
$=\frac{1}{4}\pi r^2$
$=\frac{1}{4}\times3.14\times5^2$
$=\frac{78.50}{4}$
$=19.625\ m^2$
Thus, $19.625\ m^2$ is the area of the field in which the horse can graze.
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