Q26 of 37 Page 13

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]


(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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