Question

The radii of two circles are 20 cm and 13 cm, respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.
1. 30 cm
2. 32 cm
3. 33 cm
4. 28 cm

Answer 1

Correct Answer - Option 3 : 33 cm

Given :

The radii of two circles are 20 cm and 13 cm, respectively.

Formula used :

Circumference of the circle = 2π radius 

Calculations :

Let the radius of the bigger circle be R cm 

Circumference of bigger circle = 2π R 

Circumference of circle (radius = 20 cm) = 2π × 20 = 40π 

Circumference of circle (radius = 13 cm) = 2π × 13 = 26π 

According to the question 

2π R = 40π + 26π 

⇒ R = 20 + 13 

⇒ R = 33 cm 

∴ Option 3 will be the correct answer.