Question

[3]
1.
-5. Solve the following questions. (Any one)
There are three grassfields - one of the shape of
the third one hexagonal. A cow is to be tied to a
fixed at any one vertex of the field. 1
maximum area to graze?
shelas - one of the shape of an equilateral triangle, the other square and
a. A cow is to be tied to a peg by means of a rope 6 m long. The peg is
vertex of the field. In which field should the cow be tied so that it has
on​

Answer 1

Answer:

Hexagon

Step-by-step explanation:

The area available to the cow to graze can be calculated using the formula for sector of a circle

= $\frac{\alpha}{360}$ X πr²

where ∝ = angle of the sector

r = radius of the circle

In this case, radius is equal to the length of the rope

When the cow is tied to a vertex of the equilateral triangle,

∝ = 60

⇒ Area available to graze = $\frac{60}{360}$ X π X 6² = 6π

When the cow is tied to a vertex of the square,

∝ = 90

⇒ Area available to graze = $\frac{90}{360}$ X π X 6² = 9π

When the cow is tied to a vertex of the hexagon,

∝ = 120

⇒ Area available to graze = $\frac{120}{360}$ X π X 6² = 12π

Hence, the maximum area available to graze is in case of the hexagon.