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).

**(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)

Asked by Pragya Singh | 1 year ago | 73

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

**(i)** Area of circle = πr^{2 }= \( \dfrac{22}{7}\) × 5^{2} = 78.5 m^{2}

Now, the area of the part of the field where the horse can graze

= \( \dfrac{1}{4}\) (the area of the circle) = \( \dfrac{78.5}{4}\) = 19.625 m^{2}

**(ii)** If the rope is increased to 10 m,

Area of circle will be = πr^{2} =\( \dfrac{22}{7}\)×10^{2} = 314 m^{2}

Now, the area of the part of the field where the horse can graze

= \( \dfrac{1}{4}\) (the area of the circle) = \( \dfrac{314}{4}\) = 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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