There are three grassfield one of the shape of an equilateral triangle the other square and the third one hexagonal, a cow is to be tied to a pole by means of a rope 6M long the pole is fixed at any one vertex of the field in which field should be cow be tight so that its maximum area to graze?
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Answers
Answer:
Step-by-step explanation:
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: the cow must graze in hexagonal field so that it has maximum area to graze
Step-by-step explanation:
Radius=6m
Now, equilateral triagle=60°
Square=90°
Hexagon=120°
Solution=
Area available for grazing=area of sector
= θ/ ×πr^2
360
θ/360×π×6^2
θ/360×π×36
θ/10×π m^2
Since 120>90°>60°
Though 120° is greater than any another grass field