Question

Which statements are true? Check all that apply.

The ratio of the measure of the central angle to the measure of the entire circle is StartFraction 5 Over 2 pi EndFraction.
The ratio of the measure of the central angle to the measure of the entire circle is Five-halves.
The area of the sector is 250 units².
The area of the sector is 100 units².
The area of the sector is more than half of the circle’s area.

Answer 1

True statements: 1, 3, and 5.

Reasoning:
- If the central angle is 5 radians, its fraction of the circle is 5/(2π) (since a full circle is 2π radians). So statement 1 is true; statement 2 (Five-halves = 2.5) is false.
- Sector area = (1/2) r^2 θ. With r = 10 and θ = 5, area = (1/2)(10^2)(5) = 250, so statement 3 is true and statement 4 (100) is false.
- A sector is more than half the circle when θ > π. Since 5 > π, the sector is more than half the circle, so statement 5 is true.