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

Radius of first circle = r1 = 15 cm


Radius of second circle = r2 = 18 cm


∴ Circumference of first circle = 2πr1 = 30π cm


Circumference of second circle = 2πr2 = 36π cm


Let R be the radius of the circle.


Now, we are given that,


Circumference of circle = Circumference of first circle + Circumference of second circle


2πR= 2πr1+ 2πr2


⇒ 2πR = 30π + 36π


⇒ 66π ⇒ R = 33


⇒ Radius = 33 cm


Hence, required radius of a circle is 33 cm.


2