Question:
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.
Solution:
Let the radius of a circle be r.
∴ Circumference of a circle = 2πr
Let the radii of two circles are r1 and r2 whose values are 15 cm and 18 cm respectively.
i.e. r1 = 15cmand r2 = 18cm
Now, by given condition,
Circumference of circle = Circumference of first circle + Circumference of second circle
⇒ 2πr = 2πr1 + 2πr2
⇒ r = r1 + r2
⇒ r = 15 + 18
∴ r = 33 cm
Hence, required radius of a circle is 33 cm.