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.

Answer 1

Let the radius of a circle be r.

∴ Circumference of a circle = 2πr

Let the radii of two circles are r and r whose values are 15 cm and 18 cm respectively.

i.e. r₁ = 15 cm and r₂ = 18 cm

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.