Question

if the ratio of two circles. 5:3 find the ratio of their circumference

Answer 1

Lets take radii of one circle ,r = 5 x

radii of the second circle , R = 3 x

Circumference of the first circle = 2πr = 2π × 5x

                                                 = 10πx

Circumference of the second circle = 2πR = 2π × 3x

                                                       = 6πx

Therefore , ratio of the circumference of the two circles = 10πx ÷  6πx

                                                                                     = 10 ÷ 6

                                                                                     = 5 ÷ 3 

                                                                                     = 5 : 3

Answer 2

the ratio of the radii of two circles is 5 : 3
let the common multiple be x

in case one
radius of the circle is 5x
by the formula of circumference
$2\pi \: r$
the circumference of the first circle will be 10x


In case two
the radius of the another circle will be 3x
similarly as above by using the formula to fire we get the circumference 6x

now we have the both circumferences of two circles then their ratio is

$10x \div 6x$
is equal to 5:3