A horse is tied to a peg at one corner of a square shaped grass field 15m by means of a 5m long rope.
Find
(i)The area of that part 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 5m

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19.625m2 , 58.875m2

19.5m2 , 57m2

18.625 m2 ,59.875m2

None of these

answer is A.

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Detailed Solution

Length of rope in ABCD = 5m
i) Area of sector = 𝜃 x 𝜋𝑟2
360
r = length of rope
Ө=900 , 𝜋=22
7
On substituting the value is equation (i) ,we get
Area of sector = 90
360

22x52=19.625m2
7
iii) If the rope is increased by 10 m long Area of sector HBG = new area= 90
360

x × (10) =78.5 m2
7
Now , increased area= new area - old area = 78.5 - 19.625 = 58.875 m2

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