The area of a sector of a circle is 66cm² and the angle of the sector is 60^o. Find the radius of the circle.

$3\sqrt{14}$ cm

Formula to be used

Area of a sector = \(\Pi \)\( { r}^{2 } \) x \(\Theta \)/\({360}^\circ\)

\(\Theta \) = angle of the sector

r = radius

Calculation

According to the question

\(\frac{60}{360}\) x \(\Pi \)\( { r}^{2 } \) = 66

⇒ \(\Pi \)\( { r}^{2 } \) = 66 x 6

⇒ \(\frac{22}{7}\) x \( { r}^{2 } \) = 6 x 11 x 6

⇒ \( { r}^{2 } \) = 126

⇒ r = 3\(\sqrt { 14}\) cm

Therefore, the radius is 3\(\sqrt { 14}\) cm