The area of a sector of a circle is 66cm2 and the angle of the sector is 60o. Find the radius of the circle.
Answer & explanation
Correct answer: option 4
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