Find the radius of a circle whose circumference is equal to the sum of the circumferences of two radii $15\ cm$ and $18\ cm$.

Given: A circle whose circumference is equal to the sum of the circumferences of two radii $15\ cm$ and $18\ cm$.

To do: To find the radius of the circle.

Solution:

The radii of two circles are $r_1=15\ cm$ &  $r_2=18\ cm$.
 
The radius $r$ of the circle whose circumference $C=C_1+C_2$.
 
We have $C_1=2\pi r_1$ & $C_2=2\pi r_2$.
 
$\therefore$ The resulting circumference $C=2\pi r=C_1+C_2=2\pi (r_1+r_2)$
 
$=2\pi ( 15+18)\ cm=66\pi \ cm$.
 
$\therefore$ We have, $2\pi r=66\pi$

$\Rightarrow r=\frac{66}{2}\ cm=33\ cm$.

Thus, the radius of the circle is $33\ cm$.
 

Updated on: 10-Oct-2022

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