Question : If the diameter of a circle is 14 cm, find the area of the sector of the circle whose central angle measures $60^{\circ}$.
Option 1: 18.12 cm2
Option 2: 25.66 cm2
Option 3: 38.12 cm2
Option 4: 21.66 cm2
Correct Answer: 25.66 cm 2
Solution :
The diameter of a circle = 14 cm
Radius, $r$ = 7 cm
Central angle of sector, $\theta$ = $60^{\circ}$
Area of the sector of the circle = $\frac{\theta}{360^{\circ}}× \pi r^2$
= $\frac{60^{\circ}}{360^{\circ}}× \frac{22}{7} × 7^2$
= $\frac{154}{6}$
= 25.66 cm
2
Hence, the correct answer is 25.66 cm
2
.
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