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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 (see the given figure). Find
- The area of that part of the field in which the horse can graze.
- The increase in the grazing area of the rope were 10 m long instead of 5 m. [Use π = 3.14]
Solution
i) From the figure, it can be observed that the horse can graze a sector of 90° in a circle of 5 m radius.
Area that can be grazed by horse = Area of sector OACB
`= (90^@)/360^@ pir^2`
`=1/4xx 3.14xx (5)^2`
= 19.625 m2
ii) Area that can be grazed by the horse when length of rope is 10 m long
`=(90^@)/(360^@) xx pi xx (10)^2 `
=`1/4 xx 3.14 xx 100`
= 78.5 m2
Increase in grazing area = (78.5 − 19.625) m2
= 58.875 m2
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