Question

The area of circle with center 'O' is equal to the sum of the areas of two smaller circle of radius 4.8 cm and 5.5 cm. Find the circumference of circle 'O'?
1. 14.6\(\pi\) cm
2. 11.6\(\pi\) cm
3. 14.9\(\pi\) cm
4. 13.6\(\pi\) cm

Answer 1

Correct Answer - Option 1 : 14.6\(\pi\) cm

Given:

Radius of smaller Circles = 4.8 cm and 5.5 cm

Formula used:

Area of circle = \(π r^2\)

Circumference of circle = \(2π r \)

Calculation:

Let the radius of circle O = R

∵ SUm of areas of two smaller circle = Area of circle O

⇒ \(π\)(4.8)² + \(π\)(5.5)² = ​\(π\)R²

⇒ \(π\)[(4.8)2 + (5.5)2] = ​​​​\(π\)R²

⇒ (4.8)2 + (5.5)2 = R²

⇒ 23.04 cm² + 30.25 cm² = R²

⇒ 53.29 cm² = R²

⇒ R = √53.29 cm

⇒ R = 7.3 cm

∴ Circumference of circle O = \(2π r \)

= 2 × π  × 7.3 cm

= 14.6π cm

∴ The circumference of circle is 14.6π cm