Question

A SECTOR OF 120 DEGREE CUT OUT FROM A CIRCLE HAS AN AREA OF 66/7 SQ CM.THE RADIUS OF THE CIRCLE IS ????

Answer 1

Answer on Question #47910 – Math – Geometry

A SECTOR OF 120 DEGREE CUT OUT FROM A CIRCLE HAS AN AREA OF 66/7 SQ CM. THE RADIUS OF THE CIRCLE IS ???

Solution:

$\alpha = 120{}^{\circ}$ – central angle of the sector;

$A = \frac{66}{7} \mathrm{~cm}^{2}$ – area of the sector;

$R$ – radius of the circle;

Formula for the area of the sector:

$$A = \frac{\alpha}{360{}^{\circ}} \pi R^{2}$$ $$R = \sqrt{A \frac{360{}^{\circ}}{\alpha \pi R^{2}}} = \sqrt{\frac{66}{7} \mathrm{~cm}^{2} \frac{360{}^{\circ}}{120{}^{\circ} \cdot 3.14}} = 3 \mathrm{~cm}$$

Answer: radius of the circle is equal to $3 \mathrm{~cm}$.

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