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Four horses are tethered at 4 corners of a square field of side 70 met

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Bunuel
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Four horses are tethered at 4 corners of a square field of side 70 met [#permalink] New post   07 Dec 2021, 08:45
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Four horses are tethered at 4 corners of a square field of side 70 meters so that they can just about reach one another. Find the area (in square meter) left ungrazed by the four horses.

A. 3850
B. 1075
C. 1050
D. 1200
E. 950


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C
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sanjitscorps18
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Re: Four horses are tethered at 4 corners of a square field of side 70 met [#permalink] New post   07 Dec 2021, 09:03
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Bunuel wrote:
Four horses are tethered at 4 corners of a square field of side 70 meters so that they can just about reach one another. Find the area (in square meter) left ungrazed by the four horses.

A. 3850
B. 1075
C. 1050
D. 1200
E. 950


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Since the four horses are tied to the vertices of the square filed they effectively graze out a circle ( 4 x quarter circles ) from the square. The radius of all these circles would be 70/2 = 35 meters as we are told that the horses can just about reach one another.

Hence area un-grazed = 70^2 - π x 35^2

= 4900 - 3850 = 1050

Option C
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Re: Four horses are tethered at 4 corners of a square field of side 70 met [#permalink] New post   07 Dec 2021, 11:57
The way this problem reads suggests they each can meet ALL of the others, which can only happen at the center, suggesting a radius of 35root2, producing overlapping quarter circles that is more complicated to handle

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Re: Four horses are tethered at 4 corners of a square field of side 70 met [#permalink] New post   07 Dec 2021, 19:41
Bunuel wrote:
Four horses are tethered at 4 corners of a square field of side 70 meters so that they can just about reach one another. Find the area (in square meter) left ungrazed by the four horses.

A. 3850
B. 1075
C. 1050
D. 1200
E. 950


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Square side 70 metres.
Four horses tied at four corners so that they can just reach each other means radius = rope = 70/2 = 35metres.

Now the area left ungrazed = area of square - 4*[theta(90)/360]*22/7*(35)^2
70^2 - 22*5*35
On solving we will get 1050 C as the answer.
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Re: Four horses are tethered at 4 corners of a square field of side 70 met [#permalink] New post   08 Dec 2021, 05:26
Horses are tied to the corners and can just about reach each other. The side of the field is 70 metres. So each horse can move in a radius of 35 metres in a quarter circle. To get the ungrazed area we subtract the area of 4 quarter circles from the area of the entire square field
i.e. Area (square) - 4 * Area (quarter circle)
=70*70 - 4 * (Pi * 35*35/4)
=4900 - pi*1225
= ~1500 sq metres
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Re: Four horses are tethered at 4 corners of a square field of side 70 met [#permalink]
08 Dec 2021, 05:26
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