Ex 12.2, 8 - A horse is tied to a peg at one corner of square - Ex 12.2

  1. Chapter 12 Class 10 Areas related to Circles
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Ex 12.2, 8 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 figure). Find the area of that part of the field in which the horse can graze.(Use ฯ€ = 3.14) Let ABCD be square field And ,length of rope = 5 m Hence (r) = 5 m We need to find area of field which horse can graze, i.e. area of sector QBP Note:- In square all all angles are 90ยฐ. Hence, โˆ  QBP = 90ยฐ Area of sector QBP = ๐œƒ/360ร—ฯ€r2 = 90/360ร—3.14ร—52 = 1/4ร—3.14ร—5ร—5 = (3.14 ร— 25)/4 = 19.625 Hence, Area of field which horse can graze = Area of sector QBP = 19.625 m2 Ex 12.2, 8 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 figure). Find (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use ฯ€ = 3.14) Length of the rope is increased to 10 m. Area grazed by horse now = Area of sector HBG Area of sector HGB = ๐œƒ/360ร—๐œ‹๐‘Ÿ2 = 90/360ร—๐œ‹ (10)2 = 1/4ร—3.14ร—10ร—10 = 1/4ร—314 = 78.5 m2 Thus, area grazed by horse now = 78.5 m2 Increase in grazing area = Area grazed by horse now โ€“ Area grazed previously = (Area of sector HGB โ€“ Area of sector QBP) = (78.5 โ€“ 19.625) = 58.875 m2 Hence, increase in grazing area = 58.875 m2

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