Area of Sectors of Circles

The area of a circle is given by the formula: $$A = \frac{1}{2} \times \text{r}^2 \times \theta$$ , where r is the radius and θ is the angle in radians.

The area of a sector can be calculated using the formula: $$A = \frac{1}{2} \times r^2 \times \theta$$ , where r is the radius and θ is the angle in radians.

180 degrees is equal to $$\frac{\text{π}}{1}$$ radians.

The area of the circle is $$A = \text{π} \times (5)^2 = 25\text{π} \text{ cm}^2$$ .

The area of a semicircle is half the area of a full circle: $$A = \frac{1}{2} \times \text{π} \times r^2$$ .

To convert degrees to radians, multiply by $$\frac{\text{π}}{180}$$ .

First convert 60 degrees to radians: $$60 \times \frac{\text{π}}{180} = \frac{\text{π}}{3}$$ . Then, use the formula: $$A = \frac{1}{2} \times 10^2 \times \frac{\text{π}}{3} = \frac{50\text{π}}{3} \text{ cm}^2$$ .

Convert 90 degrees to radians: $$90 \times \frac{\text{π}}{180} = \frac{\text{π}}{2}$$ . Then, use the formula: $$A = \frac{1}{2} \times 4^2 \times \frac{\text{π}}{2} = 8\text{π} \text{ in}^2$$ .

First, find the radius: r = 6 inches. The area of the pie is $$A = \text{π} \times (6)^2 = 36\text{π} \text{ in}^2$$ . Each slice area is $$\frac{36\text{π}}{8} = 4.5\text{π} \text{ in}^2$$ .

The radius is 5 inches. The area is $$A = \text{π} \times (5)^2 = 25\text{π} \text{ in}^2$$ .