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Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area.

What area will be left ungrazed? $[Take π =3 . 14 .]$

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587.5 sq. m

537.5 sq. m

547.5 sq. m

597.5 sq. m

answer is B.

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Detailed Solution

We have to find the area that will be left ungrazed when four cows are tethered at the four corners of a square field of side 50 m.
We know that,
Side of the square field is 50 m.
Considering the figure:
Question Image

Let r be the radius of the circle:

r = 502

⇒ r = 25 m

Area of square =

(side) 2

Area occupied by a sector of a circle having an angle

θ

= θ 360 × π r 2

where, r is the radius of the circle and

θ

is the sector angle.
Calculating the area that is left ungrazed:
Area left ungrazed = (Area of the square) – 4 (Area of the sector)

= 50 × 50 − 4 × 3.14 × 25 × 25 × 90360

= 2500 − 4 × 1962.5 4

= 2500 − 1962.5

= 537.5 m 2

The area that is left ungrazed is 537.5

m 2

.
Therefore, option 2 is correct.

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