There are three grassfield- one of the shape of an equilateral triangle, the other square and third one hexagonal .a A cow is to be tied to a peg by means of a rope 6 m long. The peg is fixed at any one vertex of the field. In which field should be the cow be tied so that it has maximum area to graze?
Answers
when a cow is tied to a pole of any grass field it grazes a sector of the corresponding circle at each end of the field.
Equilateral triangle Field:
in an equilateral triangle,each angle is 60°
radius=6m(given)
we know that Area of a sector of a circle=given angle/360×pi× r^2
area of the sector=60/360×22/7×6×6=1/6×22/7×6×6
=132/7=18.8m^2
Square Field:
in a square,each angle is 90°
radius=6m(given)
we know that Area of a sector of a circle=given angle/360×pi× r^2
area of the sector=90/360×22/7×6×6=1/4×22/7×6×6
=1/4×22/7×6×6=198/7=28.2m^2
Hexagonal field:
in a hexagon,each angle is 120°
radius=6m(given)
we know that Area of a sector of a circle=given angle/360×pi× r^2
area of the sector=120/360×22/7×6×6=1/3×22/7×6×6
=37.7m^2
Now, when we compare the areas , the hexagonal field has a larger are compared to the equilateral triangle and square field
Therefore the cow is able to graze maximum area in a hexagonal field so it should be tied in the hexagonal field.
hope it helps................
Answer:
hexagon
Step-by-step explanation:
the angle between two sides of a hexagon is greater than those of a triangle and a square. So, to graze the maximum angle, the cow should be put in the hexagon