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Four horses are tethered with equal ropes at 4 corners of a square field of side 70m, so that they just can reach one another. Find the area left ungrazed by the horses.

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4500 m2

1050m2

3500 m2

2000 m2

answer is B.

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Detailed Solution

Given, side of square = 70m.
The diagram will be as follows,
Question Image

So, radius is half of square i.e

702

= 35m.
So, putting the values of radius as 35 and multiply by 4,

Area grazed = 4 × 90360 × π (702) 2 ⇒ π (35) 2

Area grazed = \frac{22}{7} \times 35^{2}

⇒

3850 m^{2}

There are 4 Quarter circles in the square.
Hence, area ungrazed = area of Square - area of grazed.

⇒

{Area of square = (side)}^{2}

⇒

{(70)}^{2}

⇒

4900 m^{2}

⇒

Ungrazed area = 4900 - 3850

⇒

1050 m^{2}

Therefore, the correct option is 2.

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