M4maths Previous Puzzles

24 Nov 2015 Area

A copper wire when bent in the form of a hexagon encloses an area of 726*Sqrt(3) cm^2. If the wire is bent to form a circle, find the area enclosed by it.

OPtion

1) 1510 cm^2
2) 1426 cm^2
3) 1396 cm^2
4) 1236 cm^2
5) 1386 cm^2
6) 1358 cm^2
7) 1378 cm^2
8) 1478 cm^2
9) 1486 cm^2
10)None of these

Solution

Using area we can compute length of the side of the hexagon. Then by equating perimeter of hexagon to circumference we can get radius of circle to compute area.
We have
Area of hexagon = 726*Sqrt(3) cm^2
Let side length be a.
Area = 3*Sqrt(3)/2 * a^2 = 726*Sqrt(3)
a^2 = 484
a = 22 cm
Perimeter of hexagon = circumference (=length of wire)
6a = 2 Pi r
r = 21 cm
Area = Pi r^2
= 1386 cm^2
Option 5)

Correct Option: 5 Best Solution (24)

bhaskar   9 years AGO

1.5*sqrt(3)*a*a=726*sqrt(3)
a=22
6a=132
132=2*pi*r
r=21
area=pi*r*r=1386

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Deepak kumar singh   9 years AGO

6* sqrt(3)*a^2/4=726*sqrt(3)
=> a=22
perimeter of hexagon=perimeter of circle
=> 6*22=2*pi*r
=>r=21
Area of circle= Pi*(21)^2
= 1386

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ABHINAV PUSHPAM   9 years AGO

area of hexagon = 3sqrt(3)*a^2/2
726sqrt(3)= 3sqrt(3)*a^2/2
so, A= 22cm
perimeter of hexagon = 6*22= 132
perimeter of hexagon = circumference of circle
2pi*r= 132
r=21
now, area = pi*r^2= 1386 cm^2
option 5)

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poojasaisri   9 years AGO

area of hexagon=(3*sqrt(3)/2)*a^2
given area of hexagon=726*sqrt(3)
by solving we get a=22
circumference of circle= perimeter of hexagon
2*pi*r=6*a
solving r=21
area of circle=pi*r^2
=(22/7)*21*21
=1386 cm^2

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MRITUNJAY   9 years AGO

area of hexagon = 3sqrt(3)*a^2/2
726sqrt(3)= 3sqrt(3)*a^2/2
so, A= 22cm
perimeter of hexagon = 6*22= 132
perimeter of hexagon = circumference of circle
2pi*r= 132
r=21
now, area = pi*r^2= 1386 cm^2
option 5)

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RAHUL KUMAR   9 years AGO

area of hexagon = 3sqrt(3)*a^2/2
726sqrt(3)= 3sqrt(3)*a^2/2
so, A= 22cm
perimeter of hexagon = 6*22= 132
perimeter of hexagon = circumference of circle
2pi*r= 132
r=21
now, area = pi*r^2= 1386 cm^2
option 5)

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Pooja Shaw   9 years AGO

area of hexagon=(3sqrt3/2)a^2=726*sqrt3
by solving this we will get a=22
thus circumference of the circle=22*6=132
132=2piR
solving this we will get R=21.008
then calculating the area piR^2=pi(21.008)^2=1386 cm^2
thus 5)1386 cm^2 is the correct answer

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NAVEEN KUMAR   9 years AGO

area of hexagonal=(3*sqrt(3)*S)/2=726*sqrt(3)
so, S=22 c.m
perimeter of hexagonal=perimeter of circle=2*pi*r
=>22*6=2*(22/7)*r
=>r=21cm
Hence,Area of circle=(22/7)*21*21=1386 cm^2

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Isha Saxena   9 years AGO

given area of hexagon=726*sqrt(3) cm2
and area of hexagon=3*sqrt(3)*(1/2)*(a^2) cm2
solving the above equation we get a=22 cm
where a is the length of a side of hexagon
thus the total length of the copper wire=22*6=132 cm
now for a circle
2*(22/7)*radius=132 cm
thus radius=11*6*(7/22)
=21 cm
thus area =(22/7)*(radius^2)
=(22/7)*21*21
1386 cm^2=answer

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Jaikumar Bhatia   9 years AGO

Area of Hexagon=[3*Sqrt(3)/2]*a^2......(a is side of hexagon)
726*Sqrt(3)=[3*Ssrt(3)/2]*a^2...............(i)
Simplify (i)
a=Sqrt(484)
Perimeter of hexagon=6*a=6*Sqrt(484)...................(ii)
Perimeter of Circle=Pi*d=Perimeter of Hexagon.....(iii)
Pi*d=6*Sqrt(484)....................................from (ii)&(iii)
d=(6/Pi)*Sqrt(484).....................................(iv)
Area of Circle=(Pi/4)*d^2
=1386..............................(by putting the value of 'd' from (iv)
So ans is 1386Cm^2
Option is (5)

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Nandkishor jaiswal   9 years AGO

area of hexagon is = 3/2*sqrt(3)*a*a
or, 726*sqrt(3)=3/2*sqrt(3)*a*a
a=22 cm
so side of hexagon= 22 cm
now perimeter of hexagon=perimeter of circle
or, 6*a=2*pi*r
or, 6*22=2*pi*r
so, r=21
now area of circle will be
pi*21*21=1386

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ashok   9 years AGO

side length of hexagon=22(since hexagon forms six equilateral triangles)
radius of circle=66*7/22(length of the wire equal to perimeter of circle)
hence area=1386

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ramakrishnateja   9 years AGO

are aof hexagon is 726 sqrt(3).
but we know that area is 3 sqrt(3)l^2/2. so, equating two we get l^2=484. l=22. perimetr=6l=6*22.
for cirlce it is 2*pi*r=6*22. hence r=6*22/2*pi.
are of circle ispi*r^2=1386cm^2.

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Shubham Raj   9 years AGO

area of hexagon=(3*sqrt(3))* a^2/2
so,side of hexagon=22 cm
perimeter=22*6=132 cm =perimeter of circle=2r*3.14
so,,radius of circle=66/3.14
area of circle=1387.26

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Rhythm   9 years AGO

6x area of equilateral triangle=726sqrt(3).
side= 22cm
length of wire=132cm
area of circle= 1386 cm^2

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sumit kumar   9 years AGO

a/c to question
6*area of equilateral triangle=726*3^(1/2)
side=22cm
now have to find length of copper wire which is 22*6=132 cm
radius of circle which will form with same length
so, 2*22/7*r=132
r=21 cm
therefore, area enclosed by circle is 22/7*r^2=1386 cm^2.

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bhargavi b s   9 years AGO

by using the given data we can find side of the hexagon i.e.,a=22.by using this side we can find perimeter of the hexagon p=6(22)=132 that itself the perimeter of circle using that we can find radius r=21 finally the area of cicle a=1386 cm^2

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Saurabh Agrawal   9 years AGO

area of hexagon = (3 *sqrt(3)*a^2)/2=726*sqrt(3)cm^2
rom eq. =22cm
perimeter of hexago = 6*a=6*22=132cm=perimeter of circle
132=2*22*r/7
r=21cm
area of circle =(22*r^2)/7
area= (22*21^2)/7=1386cm^2

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shubham gupta   9 years AGO

726sqrt3÷(sqrt3/4)=a^2

A=22
So perimeter or hexa is 6*22=132

132=2'π४
४=21
Area =π४^2
=1386

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Devendra Marghade   9 years AGO

If side of hexagon=a, then Area=(3/2)*Sqrt(3)*a^2=726*Sqrt(3)
a=22 and total length of side=6*a=6*22=132=Perimeter of circle.
So 2*Pi*R=132, R=132/(2*Pi)=66/Pi
Area enclosed by circle=Pi*R^2=Pi*[66/Pi]^2=66^2/Pi=1386
Option 5)

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Mukul   9 years AGO

Area of Hexagon = 3*sqrt3*a/2
a = sqrt(484)
perimeter of hexagon = 6*a
perimeter of circle = 2*pie*r
since we are using same copper wire,
6*a=2*pie*r
hence, r= 3*a/pie where a = sqrt(484)

Now, area of circle = pie*r*r
putting the value of r and a we get the area of circle to be,
1386.55 cm^2

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N.Vennela Rani   9 years AGO

area of hexagon=(3*3^(1/2)*a^2)/2=726*3^1/2
=>a=22,perimeter of the hexagon=6a=132
perimeter of the circle=2*pi*r=132
=>r=21.02
=>pi*r^2=1386 cm^2

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Surabhi Yadav   9 years AGO

Area of hexagon=(3*sqrt3)/2*side square
726*sqrt3=(3*sqrt3)/2*side square
side(a)=22cm
Perimeter of hexagon=6a
=6*22=132cm
Area of circle=Perimeter of hexagon
2*pi*radius=132
radius(r)=21cm
Area of circle=pi*r*r
=22/7*21*21
=1386cm^2

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Jamil Ahmed   9 years AGO

Each side of the hexagon = sqrt {726*sqrt(3)*4/6*sqrt(3)}
=22 cm

Length of the wire = Perimeter of the hexagon = 22*6 = 132 cm

Hence, radius of the circle = 132*7/2*22 = 21 cm

Therefore, area of the circle = 22*21^2/7 = 1386 cm^2

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