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Question

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
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π=3.14)
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Solution

Side of square field =15 m

Length of rope =5 m=radius of the quadrant

The area available for the horse to graze = Area of Quadrant of a circle
Area of Quadrant having radius 5 cm =π×r24
=3.14×5×54

=78.54

=19.625m2
If the length of rope is increased to 10m, then the new radius =5+5=10 m
Area of new quadrant having radius 10 cm =π×r24
=3.14×10×104
=3144
=78.5m2
Increase in grazing area = Area of new quadrant having radius 10 cm Area of Quadrant having radius 5 cm
=78.519.625=58.875m2

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