 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says in the given figure a horse is tied to a peg at one corner of a square shaped grass field of side 15 meter by means of a five meter long rope. Fine one the area of that part of the field in which the horse can graze to the increase in the grazing area if the rope for 10 meter long instead of 5 meter. The given problem is based on the area of a sector and we know that the area of the sector of angle theta is equal to theta upon 360 into pi r square where r is the radius of the angle of the sector in degrees. So this is a key idea behind our question the help of this key idea to solve the above question. So let's start the solution part 1 In the given figure a horse is tied to a peg at one corner of a square shaped grass field of side 15 meter. It means the side of the square is 15 meter by means of a 5 meter long rope. So the horse is grazing this sector where the angle of the sector is 90 degree because it is a square shaped grass field and the length of the rope is 5 meter that is the radius of this sector is 5 meter. From the given figure sector that is theta is equal to 90 degree and radius of this sector is the area of the field in which the horse can graze equal to area of this sector of radius 5 meter and angle of this sector that is theta is equal to 90 degree and according to our key idea it is equal to theta upon 360 into pi r square now theta is 90 degree. So this is equal to 90 upon 360 into 3.14 into 5 into 5 meter square. So on cancellation we have and this is equal to 1.57 into 25 meter square upon 2 and this is again equal to 39.25 upon 2 meter square and this is equal to 19.625 meter square. Hence the answer for part 1 is 19.625 meter square. Let's move to the part 2 now in part 2 we have to find the increase in the grazing area if the rope for 10 meter long instead of 5 meter. So when the length of rope increased in meter then r is equal to 10 meter. So the new area the horse can graze when radius is 10 meter and angle of the sector is 90 degree is equal to 90 upon 360 into pi that is 3.14 into r square 10 into 10 meter square. So we have this is equal to 3.14 into 100 upon 4 meter square or this is equal to 3.14 upon 4 meter square and this is again equal to 78.5 meter square. So when the radius was 5 meter the grazing area was 19.625 meter square, but when the radius is 10 meter then the grazing area is 78.5 meter square. Hence the increase in the grazing area equal to 78.5 minus 19.625 meter square and this is equal to 58.875 meter square. Hence the answer for part 2 is 58.875 meter square. Hope the solution is clear to you. Buy and take care. Thank you.