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**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.**

Answer:

As the horse is tied at one end of a square field, it will graze only a quarter (i.e. sector with θ = 90°) of the field with radius 5 m.

Here, the length of rope will be the radius of the circle i.e. r = 5 m

It is also known that the side of square field = 15 m

Area of circle = πr^{2} = 22/7 × 5^{2} = 78.5 m^{2}

Now, the area of the part of the field where the horse can graze = ¼ (the area of the circle) = 78.5/4 = 19.625 m^{2}

If the rope is increased to 10 m,

Area of circle will be = πr^{2} =22/7×10^{2} = 314 m^{2}

Now, the area of the part of the field where the horse can graze = ¼ (the area of the circle)

= 314/4 = 78.5 m^{2}

∴ Increase in the grazing area = 78.5 m^{2} – 19.625 m^{2} = 58.875 m^{2}

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