a horse is tied to a peg at one corner of a square shaped grass field of side 15m by means of a 5m long rope.find the area of that part of the field in which the horse can graze.
19.6 (to three significant figures)
well , think about this. if a point is given , and you are asked to go 5m from it, you can go left ,or right or wherever within the given 5m. there are infinite possible ways to be %m away from that piont. if you connect all these points, you get a circle. so if you were asked to find the area bound by the circle, well you easily can.
now in this problem there is a square field. eventhough it can move about a circle, it can only graze within the field. so the area you have to find is the one quarters of the circle inside the field.
that would be:
where r= 5m
substituting this, you get 19.6 (or) 25π/4
hope that helps :)
length of rope = 5m
hence r= 5m
area of sector = ○/360°×3.14×5×5
HOPE IT HELPS YOU