Question

area of two circles are in ratio 16 :81 find ratio of their circumference​

Answer 1

area of circle = π r²
Let the radius of first circle is r units
and the radius of second circle be R units
area of first circle = πr²
area of second circle = πR²
A/q
(πr²)/(πR²) = 16/81
⇒r²/R² = 16/81
⇒r/R = 4/9______(1)
now, circumference of first circle = 2πr
circumference of second circle = 2πR
ratio, (2πr)/(2πR) =r/R = 4/9_______(from equation 1)

Answer 2

Area of two circles = 16 : 81
 ie     pi * r1^2 : pi * r2^2 = 16:81
               r1^2 : r2^2  = 4^2 : 9^2
                    r1 : r2  =  4 : 9
Circumference  = 2*pi*r1 : 2*pi*r2 
                           = r1  :  r2
                            = 4 : 9