Question

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 fig. 2). Find
(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 10m
long instead of 5m.(Use t = 3.14)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

$side \: of \: squre \: = 15m \\ length \: of \: rope \: = radius \: of \: sector = 5m \\ area \: of \: the \: part \: of \: field \: in \: \: which \: horse \: can \: graze = area \: of \: sector \\ = \frac{90}{360} \times \pi {r}^{2} \\ = \frac{90}{360} \times 3.14 \times {5 }^{2} \\ = \frac{1}{4} \times \frac{314}{100} \times 25 \\ = \frac{1}{4} \times \frac{314}{4} \\ = 19.625 {m}^{2} \\ now \: new \: radius \: = 10m \\ area \: of \: part \: of \: field \: in \: which \: the \: horse \: can \: graze = \frac{90}{360} \times 3.14 \times 10 \times 10 \\ = \frac{1}{4} \times 314 \\ = 78.5 {m}^{2} \\ increase \: in \: part \: of \: field = 78.5 - 19.625 \\ = 58.875 {m}^{2}$

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