- 11 cm
- 10 cm
- 9 cm
- 8 cm

Option 3 : 9 cm

**Given:**

Sum of areas = 202π

Distance between centers = 20 cm

**Formula used:**

Area of circle = πr^{2}

**Calculation:**

The circles touch externally i.e. sum of radii is 20 cm

Let the radius of the bigger and smaller circle be R and r respectively

∴ R + r = 20

A.T.Q

πR^{2} + πr^{2} = 202π

⇒ R^{2} + r^{2} = 202

⇒ R^{2} + (20 - R)^{2} = 202

⇒ R^{2} + 400 + R^{2} - 40R = 202

⇒ 2R^{2} - 40R + 198 = 0

⇒ R^{2} - 11R - 9R + 99 = 0

⇒ R = 11,9

Radius of smaller circle = 9 cm

**∴ The radius is 9cm**

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 2,17,00,894+ Students

Testbook Edu Solutions Pvt. Ltd.

1st & 2nd Floor, Zion Building,

Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

[email protected]
Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

Toll Free:1800 833 0800

Office Hours: 10 AM to 7 PM (all 7 days)