A horse is tied to the corner of a square of side 15 m with a rope of length 14m.Find the area of which the horse can graze and the area which it cannot?

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gdvs

  • Jul 8th, 2005
 

answer is 616 sq.m

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jahnavi

  • Sep 30th, 2005
 

208 sq.m and 17 sq.m

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Nitin

  • Dec 24th, 2005
 

Graze area = 154

Non Graze area = 71

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Rupesh

  • Feb 15th, 2006
 

Hi allThe answers are:Grazed area = pi*14*14/4 = 154.93 sq-mtsNon-grazed area = 15*15 - 154.93 = 71.06 sq-mts

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achar

  • Feb 20th, 2006
 

hi all

grazing area=(3.142*14*14)/4=153.958 Sq.mts

non grazing area=((3.142*15*15)/4)-153.958=22.7795 Sq.mts

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area of the sector (grazing area)              = (theta*3.14*14*14)/360
                                                                  = (90*3.14*14*14)/ 360
                 Area of the grazing area          = 154.86 sq.m.  
                 Area of the non grazing area   = area of the square - area of the sector
                                                                  = 225-154.86=70.14 sq.m.

Length of each side of the square is 15m. So its area = 152 sq. m. = 225 sq.m.
Now tied to a corner, the horse can graze ¼ part of the circle formed with a radius of 14m.
So the area horse can graze = (22/7) * 142 * (1/4) = 154 sq.m.
The area the horse can’t graze = (225 – 154) = 71 sq.m.

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Paapu159

  • Sep 17th, 2011
 

Answers : approx 154sq.m and 71 sq.m

The area grazed by the cow will be in the shape of a sector of the circle.. i.e length of the rope will be the radius and angle is 90 degrees........
Area of sector will be 0.5 * angle * (pi/180) * radius * radius = 0.5 * 90 * (pi /180)* 14 *14 = 153.93803
i.e area grazed by cow = 153.93803 sq. m
Area that cow cannot graze = Total area - area grazed by cow
Here, total area is nothing but the area of the square i.e 15*15 = 225 sq.m
Thus area that cannot be grazed by cow = 225 - 153.93803 =71.06917 sq.m

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Rajkumar

  • Oct 30th, 2015
 

Area of grazing is 153.86 sq.m not 154.86. Hence answer is 71.14 sq.m

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Devaraj Vignesh

  • Aug 9th, 2017
 

Area of Square is a*a that is 15*15 = 225.
Total grazing area = 225 square metres.
Area of grazing
Since the horse is tied to the corner, the horse can move in a direction of a quarter-circle (half semi-circle).
Area of circle is pi*r*r.
Since the area to be found is for a quarter circle, pi*r*r/4.
That is, 22/7*14*14/4 = 154.
So, total grazing area is 154 square metres.
Area which it cannot graze is 225-154 = 75 sq.m.
Hence Proved!!!

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Saish Datta

  • Aug 31st, 2017
 

Consider
the area of circle = 22/7 * 14 * 14
the area of square = 15*15=225
Area of the Circle formed inside the square = 1/4(area of circle)// angle b/w adjacent sides in a square is 90 degrees//
=1/4*22/7*14*14 = 11*14=154
the area of which the horse can graze is 154 and the area which it cannot is 225-154=71

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Himanshu Priyadarshi

  • Sep 5th, 2017
 

Area of square = 15*15=225
Area that horse graze = 22/7*7*7/4=154
Area that horse has not grazed = 225-154=71

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Balloo

  • Oct 30th, 2018
 

154 and 71

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BSmith

  • Jun 25th, 2022
 

Area of square = 15*15 = 225
Radius of travel = 14m
Area of circle = 14*14*3.14 = 615.44
Grazing area = 615.44*0.25 = 154
non-grazing area = 225-154 = 71

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