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.

• 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
• 10 years agoHelpfull: Yes(52) No(2)
• 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
• 10 years agoHelpfull: Yes(10) No(1)
• @ Rakesh
  Hello Bro, i think u r very good in geometry can u plz tell us from which material u learn geometry???
• 10 years agoHelpfull: Yes(5) No(2)
• 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
  
• 10 years agoHelpfull: Yes(2) No(0)
• 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.
• 10 years agoHelpfull: Yes(1) No(0)
• Rakesh apka length of arc ka formula galat hai but approach sahi hai or answer bhi
• 10 years agoHelpfull: Yes(1) No(4)
• 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
• 10 years agoHelpfull: Yes(0) No(4)
• 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
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• theta=arc/rad;
  suppose arc=x;
  45=x/r1;
  30=x/r2;
  =>r1/r2=2/3;
  =>r1^2/r2^2=4:9
• 8 years agoHelpfull: Yes(0) No(0)
• 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
  
• 8 years agoHelpfull: Yes(0) No(0)
• 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
  
• 8 years agoHelpfull: Yes(0) No(0)