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

1 Answer

Solution :-

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\( \dfrac{22}{7}\) × 52 = 78.5 m2

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 m2

 

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

Area of circle will be = πr2 =\( \dfrac{22}{7}\)×102 = 314 m2

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 m2

Increase in the grazing area = 78.5 m2 – 19.625 m2 = 58.875 m2

Answered by Abhisek | 1 year ago

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