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