A sector of circle of radius equal to one fourth of the diagonal of square is cut from the square ta

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07 May 2014 Solve

A sector of circle of radius equal to one fourth of the diagonal of square is cut from the square taking one corner of the square as centre. If side of the square is 4 cm. then area of the remaining part is

OPtion

1) 15.68 cm^2
2) 14.43 cm^2
3) 12.78 cm^2
4) 10.34 cm^2
5) 14.73 cm^2
6) 13.14 cm^2
7) 14.14 cm^2
8) 11.88 cm^2
9) 11.83 cm^2
10)None of these

Solution

Diagonal of the square = 4√2 cm.
Hence radius of the circle = 4√2/4 cm. = √2 cm.
Area of the sector of circle = 1/4 (π* radius2)
= 1/4 (π* (√2)2 )
= π/2
Area of the square = 4*4 = =16 cm.2
Hence area of remaining part = 16- (π/2) cm.2
= 14.43 cm^2

Option 2)

Correct Option: 2 Best Solution (27)

PAWAN KUMAR   10 years AGO

4^2-(3.14*(2^1/2)/4)=14.43 cm^2

Like? Yes (1) | No   

Nimisha Pandey   10 years AGO

area of sector=90/360*2
area 0f square=16
remaining area=area of sqr-area of sector=14.43

Like? Yes (1) | No   

chandan jha   10 years AGO

16-3.14*1/2=14.43;

Like? Yes (1) | No   

Param Kothari   10 years AGO

Two adjacent sides of a square and its diagonal form
a 45-45-90 triangle
Thus diagonal = (Root of 2)* side Threfore diagonal = 4(Root of 2) cm
Therfore radius of circle =1/4 * diagonal=0.25*4(Root 2)=(root 2)
Angle of the sector=90
Thus its area=(90/360)*3.14* (Root 2)^2
=2*3.14*0.25
=1.57
Area of square= side^2 = 4^2= 16
Therefore area of remaining part = 16 - 1.57
=14.43 cm

Like? Yes (1) | No   

Dr.Dipin Singh   10 years AGO

Area of square = 4*4=16 cm^2
diagonal of square = Sq root (4^2+4^2)= 4 Root 2
radius of circle taking one corner of the square as centre= (4 root 2)/4= root 2.
Area of remaining part = 16- (pi*(root2)^2)/4= 14.43 cm^2

Like? Yes (3) | No (3)  

MD SOHAIL AKHTER   10 years AGO

side of the square =4cm
diagnol of square= 4√2cm
diameter of square= 4√2/4=√2cm
area of circle under square= π*(√2)^2*(1/4)
=π/2 cm
area of remaining part in square= 4^2-1.57=14.43cm
ans option(2)

Like? Yes (3) | No (3)  

Ann Theressa   10 years AGO

Side of square, a = 4cm
diagonal of square = a*sqrt(2)
=4*sqrt(2)

Radius of sector,r = 1/4 of diagonal
= 1/4*4*sqrt(2)
=sqrt(2)

Area of sector = n/360*pi*r^2
=90/360*pi*r^2
=1/4*22/7*2
11/7

Area of square = a^2
=4^2
=16

Area of remaining part = 16-11/7
=101/7
=14.43 cm^2

Like? Yes (3) | No (4)  

azharshahid01@gmail.com   10 years AGO

Side of the Square=4
So, diagonal of square= Square root of (4^2+4^2)= Square root (32)
Radius of circle is 1/4th of diagonal. So radius= square root(32)/4
Area of circle = 3.14*(32/16)= 6.28.
Circle center is a corner of square so 1/4th of circle will be in square.
Circle 1/4th area= 6.28/4= 1.57

Area of square= 4*4= 16
Area of remaining square which is not covered by circle= 16-1.57 = 14.43

Like? Yes (2) | No (4)  

SriS   10 years AGO

total area of circle is -- 6.28cm^2
sector area is -- 1.57cm^2

so remaining area of circle is = 4.71cm^2
total area of square is = 16cm^2
remaining area of square is = 16-1.57 = 14.43cm^2

Like? Yes (1) | No (3)  

muni   10 years AGO

square radius is 2 so diagonal is 4 sqrt(2)
one corner is the center so it covers 90 degrees with sqrt(2) radius area in square.
required area= square area- sector area
=16-1.57( formula: sectorangle/2 * pi/180* r^2 )=14.43

Like? Yes (1) | No (3)  

Gitanjali K   10 years AGO

let radius of circle=r cm
diagonal of square=d cm
side of square=a cm

given, radius of circle equal to one fourth of the diagonal of square
so r=(1/4)d ...eq(1)
and d=2^1/2 * a
d=2^1/2 * 4 (given side of square=4cm)
therefore d=5.66 cm
put value of d in eq(1) we get
r=1.415 cm

Now, area of square=(side)^2
=4^2
=16 cm^2

And area of sector=(1/2)*angle in radian*(radius)^2
=(1/2)*(90*pi/180)*(1.415)^2
=1.57 cm^2

so,area of the remaining part is =(16-1.57)cm^2
=14.43 cm^2
so option (2) is the answer

Like? Yes (1) | No (3)  

KAUSTUBH BHARDWAJ   10 years AGO

AREA OF REMAINING PART=(AREA OF SQUARE)-((3.14)*(R^2)/4)
SO AREA OF SQUARE=16
2ND PART=3.14*2/4=1.57
SO
AREA OF REMAINING PART=16-1.57=14.43CM^2

Like? Yes (1) | No (3)  

gaurav arora   10 years AGO

ans is 16-1.57=14.43

Like? Yes (1) | No (3)  

Satish Zod   10 years AGO

(4^2) - ((((Sqrt(4^2+4^2))/4)^2)*22/7)/4 = 14.43

Like? Yes (1) | No (3)  

khushboo singh   10 years AGO

side of square= 4cm
so r=sqroot(2)*4/4=sqrt(2)
as corner of square is centre =>sector makes angle *area of circle
so area remaining=(4)^2-(1/4)(3.14*sqrt(2)*sqrt(2))
=14.43

Like? Yes (1) | No (3)  

harshal agrawal   10 years AGO

16-(.25*3.14*sqrt2)
= 14.43

Like? Yes (1) | No (3)  

Md.Sultan Khichi   10 years AGO

side of square =4cm
so diagonal=4 sqrt(2)
so radius=sqrt(2)
area of circle=pi*r^2=6.28
Hence area of that sector of circle will be 1/4*(6.28)=1.57
so.area of remaining part of the square=16-1.57=14.43cm^2..ans

Like? Yes (1) | No (3)  

P Dhananjaya Dora   10 years AGO

it is given that side of a square is 4 cm.
diagonal^2=32
radius^2=2
remaining area=area of square-area of sector
=16-(22*radius^2*angle of sector/7*360)
angle of sector is 90 as one of the corner is the center of the circle
solve the above

Like? Yes (1) | No (3)  

indrajeet yadav   10 years AGO

radius of circle=1/4*diagonal of square
=1/4*4sqrt(2)
=sqrt(2)
area of reamining part=total area of square-area of sector of circle=(4)^2-pi*[sqrt(2)]^2*90/360
=16-pi*2*1/4
=16-pi*1/2
=16-1.57
=14.43 cm^2

Like? Yes (1) | No (3)  

Praful   10 years AGO

Area of square = 4*4 =16 cm2
Area of sector = (90/360)*3.14*[sqrt(2)]2 = 1.57 cm2
Remaining area = 16-1.57 = 14.43 cm2

Like? Yes (1) | No (3)  

RAKESH   10 years AGO

r= d/4 = √2x/4 = √2*4/4 = √2
area of sector = pi*r^2/4 = pi/2 = 1.57

area of remaining part = 4^2 - 1.57 = 14.43 cm^2

Like? Yes (1) | No (4)  

SHEREENA NISHAD   10 years AGO

required area = area of square - area of sector
area of square = 16
area of sector = (angle of sector /360)* pi * r^2
angle of sector = 90
radius, r = d/4 where d is diagonal of square and d= side of square * square root (2)= 4*sq. root of(2)
r = sq. root (2)
r^2 = 2
req. area = 16- (90/360)* (22/7)* 2
= 16 - (11/7)
= 14.43 cm^2

Like? Yes (1) | No (4)  

Devendra Marghade   10 years AGO

As 1/4 of the diagonal of square=radius of circle
So,Radius of a circle=(1/4)*Sqrt[4^2+4^2]
=(1/4)Sqrt(32) =Sqrt(2)
Area of a sector of a circle at corner of square
=(1/4)*Pi*[Sqrt(2)]^2=(1/4)*(22/7)*2=11/7
Area of the remaining part of a square=4^2-(11/7)
=101/7 =14.429

Like? Yes (1) | No (4)  

Mukesh Nayal   10 years AGO

remaining area=16-3.14/2=14.43

Like? Yes (1) | No (4)  

ABHOY KUMAR   10 years AGO

radius of sector=r
side of square=s
diagonal(d)=s*sqrt(2)
r=1/4*d
r=1/4*(4*sqrt(2))
r=sqrt2
remaining area(A)=(area of square)-(area of sector)
A=(4^2)-(1/4*(3.14*2))
=14.43cm^2

Like? Yes (1) | No (4)  

rajani   10 years AGO

side of square=4cm
radius of circle=1/4*sqrt(4^2+4^2)=sqrt(2)cm
area of sector is 1.57cm^2
and the total area of square=16cm^2
Now the remaining part will be
16-1.57=14.43cm^2

Like? Yes (1) | No (4)  

srilakshmi   10 years AGO

diagonal of square is 4*sqrt2
radius of circle is -- sqrt2 cm
total area of circle is -- 6.28cm^2
sector area is -- 1.57cm^2

so remaining area of circle is = 4.71cm^2
total area of square is = 16cm^2
remaining area of square is = 16-1.57 = 14.43cm^2

Like? Yes (1) | No (4)