Four Horses are tethered at four corners of a square plot of side 63 metres, so that they just canno

Shiva Sharma   9 years AGO

Area of square is 63*63 = 3969 m^2
Area of four quarter circle is = 4*(1/4)*pi*(63/2)*(63/2) = 3118.5 m^2
so ungrazed area is = 3969-3118.5 = 850.5 m^2

Like? Yes (21) | No (8)  

Aravinth kumar   9 years AGO

The length of the rope in which the horses tied should be equal to half of the side of the
square plot so that they just cannot reach one another.
Therefore, the length of the rope is 31.5m (63/2).
The area covered by each horse should be equal to the area of sector with radius of 63/2 =
31.5m(length of the rope).
Total area covered by the four horses = 4* area of sector of radius 31.5 metres = Area of

circle of radius 31.5m.
Area left grazed by the horses = Area of square field - Area covered by four horses.
= 632 - (22/7)*31.5*31.5 = 3969 - 3118.5 = 850. sq.m

Like? Yes (15) | No (7)  

vini   9 years AGO

Area of ungrazed field = Area of square - Area of circle.
Area of ungrazed field = (63*63) - (3.14 * 31.5 * 31.5 )
Area of ungrazed field = 850.5 m^2

Like? Yes (6) | No (1)  

sudiptaa   9 years AGO

area of square = 63*63=3969 m^2
area inside the square that is grazed =4*area of quadrants of 4 circles
= 4*(1/4)*(22/7)*(63/2)*(63/2) =3118.5
area left ungrazed = 3969-3118.5=850.5

Like? Yes (4) | No (1)  

pankaj kumar   9 years AGO

solu- r^2-pi*r^2= ans(6)
63^2-3.142*(63/2)^2= 852.35m^2 approx 850.5m^2

Like? Yes (3) | No (1)  

Miriyala. siva sankar   9 years AGO

Area ungrazed = 63^2 - 4*1/4* Pi*(63/2)^2= 63^2 (1-22/28)
= 63*63*6/28
= 9*63*3/2= 63*27/2 = 850.5 sq mtr

Like? Yes (4) | No (3)  

Nonit Dua   9 years AGO

area ungrazed=total area of square(63*63)-area grazed(?r^2)
where r=63/2

Like? Yes (3) | No (2)  

santhosh   9 years AGO

required area =(63×63-4×1/4×22/7×63/2×63/2)

Like? Yes (1) | No   

SAYAN CHATTERJEE   9 years AGO

area ungazed = 63^2-4*22/7*1/4*(63/2)^2
= 850.5 m^2

Like? Yes (2) | No (2)  

RAKESH   9 years AGO

(63)^2 - pi *(63/2)^2

= 63*63 * (1- 22/28) = 850.5 m^2

Like? Yes (5) | No (6)  

Dinni   9 years AGO

The length of the rope in which the horses tied should be equal to half of the side of the square plot so that they just cannot reach one another. Therefore, the length of the rope is 31.5m (63/2). The area covered by each horse should be equal to the area of sector with radius of 63/2 = 31.5m(length of the rope). Total area covered by the four horses = 4* area of sector of radius 31.5 metres = Area of circle of radius 31.5m. Area left ungrazed by the horses = Area of square field - Area covered by four horses. = 632 - (22/7)*31.5*31.5 = 3969 - 3118.5 = 850. sq.m.

Like? Yes (2) | No (4)  

Pinku Burnwal   9 years AGO

four horses are tethered at four corner and each horse can graze one-forth of area of circle of radius 31.5m.
therefore, four horses will graze 4 times one-forth area of circle of=3.143*31.5*31.5=3118.64 sq.metre.

area of square=63*63=3969 sq.metre

therefore area ungrazed=area of square- area of circle=850.5 sq.metre

Like? Yes (3) | No (5)  

akanksha   9 years AGO

area of region grazed by the horses will be 4*{(90/360)*pi*(63/2)^2} and area of the plot will be 63^2.So ungrazed area will be total area-grazed area.so answer will be 850.5m^2

Like? Yes (2) | No (4)  

Bagmita Chanda   9 years AGO

As the sides of the square plot is 63 m, the area would be 63*63 m^2 = 3969 m^2.

and As the horses are tethered at 4 corners of the square and can't reach each other, four of them are covering atmost total 4*(1/4)*(22/7)*(63)^2 m^2 area =3118.5 m^2.

So the ungrazed area = (3969 - 3118.5) m^2 = 850.5 m^2

Like? Yes (1) | No (4)  

Chandrima Goswami   9 years AGO

Area of square = 63 * 63 = 3969 m^2

Area grazed = 22/7 * (63/2) * (63/2) = 3118.5 m^2

Area ungrazed = 3969 - 3118.5 = 850.5 m^2

So ans is option 6)

Like? Yes (1) | No (4)  

POOJA SINGH   9 years AGO

area ungrazed is given by
total area - 4*area grazed by each horse
63*63 - (22/7)*(63/2)^2
850.5m^2

Like? Yes (1) | No (4)  

Sambit Pal   9 years AGO

four horses at four corners can graze in a circular arc...and to just not meet each other they form a quarter of a circle with radius 63/2=31.5 m... so for 4 horses area grazed=area of circle of radius 31.5 m=3115.665 m sq. and total area of square field=63*63=3969 m sq. therefore area ungrazed=3969-3115.665 nearly equal to 851 m sq... nearest option is 6. so ans is 6)

Like? Yes (1) | No (4)  

Akshay Yelpale   9 years AGO

Since horses should not reach to each other.
Length of rope should be half of the side of square.
Length of Rope = 63/2 .

Area grazed by each horse = area of sector of radius 63/2.
Area grazed by 4 horses = 4 * area of sector of radius 63/2.
= area of circle with radius 63/2.

Area left ungrazed =Area of square - area of circle with radius 63/2.
= 63 * 63 - ( 22/7 * 63/2 * 63/2 )
=850.5

Like? Yes (1) | No (4)  

Archie   9 years AGO

Required area= Area of plot-Area covered by four horses
=63^2-((22/7)*(63/2)*(63/2))
=850.5

Like? Yes (1) | No (4)  

NAVEEN   9 years AGO

area of square-4(quater of circle)=3969-4(779.3125)

Like? Yes (1) | No (4)  

RAJAT KHANDELWAL   9 years AGO

area left for grazing= area of square field - area of the grazing part
= 63*63 - (22/7)*31.5*31.5 =850.5

Like? Yes (1) | No (4)  

Balamurugan A   9 years AGO

area of square 63*63=3969-->1
4 quarter circles=1circle then
area of circle=Ï€r^2
r=63/2=31.5
applying in circle formula=22/7*31.5*31.5
=3118.5----> 2
substitute 1-2 we get 850.5m^2

Like? Yes (1) | No (4)  

ABHINAV PUSHPAM   9 years AGO

Area ungrazed = 63^2 - 4*1/4* Pi*(63/2)^2= 63^2 (1-22/28) = 63*63*6/28 = 9*63*3/2= 63*27/2 = 850.5 sq mtr

Like? Yes (1) | No (4)  

Jawahar   9 years AGO

Area left ungrazed by the horses = Area of square field - Area covered by four horses.

= 632 - (22/7)*31.5*31.5 = 3969 - 3118.5 = 850. sq.m.

Like? Yes (1) | No (4)  

Patralika Mitra   9 years AGO

Area ungrazed = 63^2 - 4*1/4* Pi*(63/2)^2= 63^2 (1-22/28) = 63*63*6/28 = 9*63*3/2= 63*27/2 = 850.5 sq mtr

Like? Yes (1) | No (4)  

aditi goyal   9 years AGO

we have a square and we need to subtract 4 quaderants from it..so side*side-(pi)*r*r=850.5 m^2

Like? Yes (1) | No (4)  

Ashu Kumar   9 years AGO

AREA OF SQUARE IS=63*63m^2 , AND All 4 HORSE ARE AT 4 CORNER OF SQUARE. EACH HORSE GRAZE QUARTER PART OF CIRCLE. SO UNGRAZED AREA=63*63 -( 22*4*63*63*4)/4*7 =850.5 m^2

Like? Yes (1) | No (4)  

santosh kumar patel   9 years AGO

Area ungrazed = 63^2 - 4*1/4* Pi*(63/2)^2
= 63^2 (1-22/28)
= 63*63*6/28
= 9*63*3/2= 63*27/2
= 850.5 sq mtr

Like? Yes (2) | No (5)  

Narendra Gopi   9 years AGO

=63^2 - 4*1/4* Pi*(63/2)^2
= 63^2 (1-22/28)
= 63*63*6/28
= 9*63*3/2
= 63*27/2
= 850.5 sq mtr

Like? Yes (1) | No (4)  

abhishek kumar   9 years AGO

since there will be 4 quarter part in that field so radius of one part is 63/2. Now area of 4 quarter are 4*(3.14*31.5*31.5)/4=3118.5 so area of ungrazed part=63*63-3118.5=850.5

Like? Yes (2) | No (5)  

Surit Datta   9 years AGO

Area ungrazed = 63^2 - 4*1/4* Pi*(63/2)^2= 63^2 (1-22/28) = 63*63*6/28 = 9*63*3/2= 63*27/2 = 850.5 sq mtr
so option 6
that's it.

Like? Yes (1) | No (5)  

Veerraj Chauhan   9 years AGO

The four horses will graze in quadrants of radius = 63/2 m=31.5 m
therfore the grazed area by all the four horses will be = 4*( π * 31.5^2 * (1/4)) = 3117.245 m^2
the ungrazed area will be = 63^2 - 3117.245 = 851.755 m^2

The nearest option is 6

Like? Yes (1) | No (5)  

Pranati Kundu   9 years AGO

area of square - area of circle of radius 31.5
i.e. 63²-?31.5²
=850.5

Like? Yes (1) | No (5)  

ROHIT KUMAR   9 years AGO

Ungrazed area=Total area-(area of 4 quarter circle of radius 63/2)
=> 63*63-(1/4*4*(63/2)^2)
=>850.5 m^2

Like? Yes (2) | No (6)  

vimal tiwari   9 years AGO

total area = 63*63 = 3969

if horse can meet than the length of rope
will be equal or > to half of side i.e. 31.5

area grazed by 4 horse = 4 * (90/360 )(3.14 * 31.5*31.5);

required area = 3969 - area grazed by 4 horses = 854.3 m^2

but the horses just can't meet thus value of rope will be just less than 31.5
so and will be just less tha 853.3
i.e. 850.5 m^2

Like? Yes (1) | No (5)  

Sushmita Ghanty   9 years AGO

the area of the sqare plot= 63*63= 3969m^2
1 hosre can eat up=(1/4*22/7*63/2*63/2)m^2
as there are 4 horses so,
the area left ungrazed is= 3969 - {4*(1/4*22/7*63/2*63/2)}=850.5m^2

Like? Yes (1) | No (5)  

SOMA NARESH   9 years AGO

The length of the rope in which the horses tied should be equal to half of the side of the
square plot so that they just cannot reach one another.
Therefore, the length of the rope is 31.5m (63/2).

The area covered by each horse should be equal to the area of sector with radius of 63/2 =
31.5m(length of the rope).

Total area covered by the four horses = 4* area of sector of radius 31.5 metres = Area of
circle of radius 31.5m.
Area left ungrazed by the horses = Area of square field - Area covered by four horses.
= 63^2 - (22/7)*31.5*31.5
= 3969 - 3118.5
= 850. 5q.m.

Like? Yes (1) | No (5)