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} = \(π\)R^{2}

⇒ \(π\)[(4.8)2 + (5.5)2] = \(π\)R^{2}

⇒ (4.8)2 + (5.5)2 = R^{2}

⇒ 23.04 cm^{2} + 30.25 cm^{2} = R^{2}

⇒ 53.29 cm^{2} = R^{2}

⇒ 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**