The ratio of the radii of two wheel is 2:5. What is the ratio of their circumferences ?

Given: The ratio of the radii of two-wheel is 2:5

To do: Find the ratio of their circumference.

Solution:

Let the two radii be $r_1,r_2$

$ r_1  :  r_2    =   2 : 5$

Circumference of circle  =  2πr 

The ratio of their circumferences  =   $2πr_1 :  2πr_2$  

                                                                       = $2π (2)  :  2π (5)$             [ Substitute the ratios of radii in formula]

                                                              =   2  :  5                              [2π and 2π gets cancelled, since they are same]

So, the ratio of their circumferences  =  2: 5