Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:

(1) 1050 sq.m (2) 3850 sq.m
(3) 950 sq.m (4) 1075 sq.m

• area ungrazed is given by
  total area - 4*area grazed by each horse
  = 70*70 - 4*(90/360)*pi*(70/2)^2
  as the angle made by the horse is 90 degree, so applying the area of the sector,= theta/360*pi*radius^2 above
  = 70*70 - pi*(70/2)*(70/2)
  = 70*70 { 1- pi/4}
  = 70*70{6/(7*4)} , expanding pi = 22/7
  = (70*70*6) / (7*4)
  = 1050 sq m
  so answer is option 1
• 9 years agoHelpfull: Yes(26) No(0)
• Area grazed by one horse=(90/360) pi (35)^2=962.5m^2
  total area grazed by 4 horses=962.5*4=3850 m^2
  Area left=1050 m^2
• 9 years agoHelpfull: Yes(4) No(0)
• Area of each sector = (π*r^2*angle)/360°
  On solving for 4 sectors = 4*(π*35^2*90°)/360°
  On solving area of 4 sectors = 3850
  Reqd. Area = (70*70)-3850 =1050 sq.m
• 9 years agoHelpfull: Yes(1) No(0)
• each horse can graze 1/4 th of a circe i.e.., pi r^2 /2
  and 4 horses total multiplied by 4 3850
  area of square 70 ^2 =4900
  ungrazed area 4900-3850=1050
• 7 years agoHelpfull: Yes(0) No(0)
• Area of circle= Pi x r^2
  in given case there are 4 quadrants at the each corner of the square. so it is equal to a circle.So we can make use of this formula directly.
  So the required area will be = total area - area of circle= (70*70) - (Pi*35*35)= 4900-3850=1050sq.m
• 7 years agoHelpfull: Yes(0) No(0)