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A horse is tied to a pole at one corner of a square grass field of side 15 m using 10 m long rope. Find

(i) the area of that part of the field in which the horse can graze. 

(ii) the decrease in the grazing area if the rope was 5 m long instead of 10m. [Use π=3.14]

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Best answer

(i)

Let ABCD be square field

and length of rope, r = 10m

We need to find the area of the field which horse can graze, i.e. the area of sector QBP

As we know that in a square all angles are of 90°

Hence, ∠QBP = 90°

= 78.5 m2

Hence, the area of the field which horse can graze = 78.5 m2

(ii) the decrease in the grazing area if the rope was 5 m long instead of 10m

Length of rope is decreased to 5m

Area grazed by a horse now = Area of sector HBG

= 19.625 m2

So, the decrease in the grazing area

= Area of sector QBP – Area of sector HBG

= 78.5 – 19.625

= 58.875 m2

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