Question

What is the area of a sector whose arc subtends a ${30}^{\circ }$ angle at the center of a circle of radius 12 inches?

• A. $144\pi inche{s}^2$
• B. $12\pi inche{s}^2$
• C. $6\pi inche{s}^2$
• D. $24\pi inche{s}^2$

Answer 1

The correct option is B $12\pi inche{s}^2$

Area of the sector $=\frac{\theta }{{360}^{\circ }}\times \pi r^2$

For the figure given,
$\theta ={30}^{\circ }$ and $r=12inches$

Area of the sector $=\frac{{30}^{\circ }}{{360}^{\circ }}\times \pi \times (12{)}^2$

Area of the sector $=\frac{1}{12}\times \pi \times (12{)}^2$

Area of the sector $=12\pi inche{s}^2$