Latest Elitmus Aptitude Question SOLUTION: a circle A is of arc length at 45°, is same arc length at 30° of another circle B.then what is the area of circle A to circle B.

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(#M40033535) ELITMUS Numerical Ability question circle Keep an EYE

a circle A is of arc length at 45°, is same arc length at 30° of another circle B.then what is the area of circle A to circle B.

Asked In Elitmus dhanraj kumar (10 years ago)

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RAKESH  (10 years ago)

arc length = pi*r*(theta)/180
let Ra & Rb the radii of A & B respectively
=> pi*Ra*45/180 = pi*Rb*30/180
=> Ra/4 = Rb/6
=> Ra/Rb = 2/3
area of circle A to circle B = pi*(Ra)^2/pi*(Rb)^2 = (Ra/Rb)^2 = (2/3)^2 = 4:9

Is this solution Helpfull? Yes (52) | No (2)  

sanjana  (10 years ago)

The length of an arc is=
(degrees in the arc/360)*2*pi*r

suppose r1 and r2 represents the radius of the circle A and B repsectively
den
For area A
arc lenght=(45/360)*2*pi*r1
=(1/4)*pi*r1
For area B
arc length=(30/360)*2*pi*r2
=(1/6)pi*r2
given that; (1/4)*pi*r1=(1/6)pi*r2
=>pi*r1=(4/3)pi*r2
=>r1=(2/3)*r2
=>r1/r2=2/3
so Area of A/Area of B=pi*r1^2/pi*r2^2
=>AREA of A/AREA of B=r1^2/r2^2
=(r1/r2)^2
=4/9

Is this solution Helpfull? Yes (10) | No (1)  

tausif  (10 years ago)

@ Rakesh
Hello Bro, i think u r very good in geometry can u plz tell us from which material u learn geometry???

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deep chandra bhatt  (10 years ago)

theta=arc/radius
45=x/r1 r1=45/x
30=x/r2 r2=30/x
area circle A/B=pie*r1^2/pie*r2^2 =(45/x)^2/(30/x)^2=9/4

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Shireesh Mehta  (10 years ago)

Length of arc=(Circumference*angle in degrees)/360
Let r1=radius of circle A and r2=radius of circle B
Length of arc in A=(2*pi*r1*45)/360
Length of arc in B=(2*pi*r2*30)/360
Since both are the same, calculating we get,
r1/r2=2/3
Ratio of area of A to area of B=r1^2/r2^2=4:9
So, I think 4:9 should be the answer.

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ASHUTOSH KUMAR  (10 years ago)

Rakesh apka length of arc ka formula galat hai but approach sahi hai or answer bhi

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dhanraj kumar  (10 years ago)

let arc length is L at 45° of circle A,so arc length of B at 30° will be L.
so at 180 degree the arc length of circle A is same as its semi circumference which is 4L. same as ib B is 6L.
area of A/area of circle B= square of (4L/6L)=2/3
so ans 2/3

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varun dua  (10 years ago)

arc length of A=arc length of B
Q360 * pi r1^2=Q360 *pi r2^2
45360 * pi r1^2=30360 *pi r2^2
45r1=30r2
r1/r2=2/3
Area of circle A to circle B=pi*r1^2/pi*r2^2=r1^2/r2^2=4/9

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hriday  (8 years ago)

theta=arc/rad;
suppose arc=x;
45=x/r1;
30=x/r2;
=>r1/r2=2/3;
=>r1^2/r2^2=4:9

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kundan prasad  (8 years ago)

Ans: 4:9
Sol: let radius of circle of A is r1 and for B r2
Area of arc A = Area of arc B (angle of arc * radius of circle)
so pi/4*r1=pi/6*r2
r1/r2=2/3
so therefore ratio of (Area of A)/(Area of B)=(pi*r1*r1)/(pi*r2*r2)
=4/9

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AMRITANSHU SRIVASTAVA  (8 years ago)

The length of an arc is=
(degrees in the arc/360)*2*pi*r

suppose r1 and r2 represents the radius of the circle A and B repsectively
then
For area A
arc lenght=(45/360)*2*pi*r1
=(1/4)*pi*r1
For area B
arc length=(30/360)*2*pi*r2
=(1/6)pi*r2
given that; (1/4)*pi*r1=(1/6)pi*r2
=>pi*r1=(4/3)pi*r2
=>r1=(2/3)*r2
=>r1/r2=2/3
so Area of A/Area of B=pi*r1^2/pi*r2^2
=>AREA of A/AREA of B=r1^2/r2^2
=(r1/r2)^2
=4/9

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