A sector is defined by two ___ and the arc they create.

Radii

True or False: A segment of a circle is formed between a chord and the arc it subtends.

True

The area of a sector with angle θ and radius r is calculated using the formula ___.

(θ/360) × π × r²

If the angle of a minor sector is 60°, what is the angle of the corresponding major sector?

300°

Calculate the area of a sector with a radius of 10 cm and an angle of 180°. What is the area?

50π cm²

True or False: The length of an arc is calculated using the formula (θ/360) × circumference of the circle.

True

If a circle has a radius of 15 cm, what is the area of the circle?

225π cm²

A major segment is defined by a ___ arc.

Major

Fill in the blank: The area of a segment is calculated as the area of the corresponding sector minus the area of the ___.

Triangle

Calculate the area of the minor segment if the area of the sector is 200 cm² and the area of the triangle is 80 cm².

120 cm²

What is the formula for the area of a triangle formed by two radii and the chord in a circle?

½ × base × height

If a chord subtends an angle of 120° in a circle with radius 7 cm, what is the area of the corresponding sector?

(120/360) × π × 7² = (1/3) × π × 49 = (49π/3) cm²

True or False: A minor segment is made by a major arc.

False: A minor segment is made by a minor arc.

What is the area of a sector with a radius of 5 m and an angle of 45°?

(45/360) × π × 5² = (1/8) × π × 25 = (25π/8) m²

Fill in the blank: The area of a major segment can be calculated by subtracting the area of the minor segment from the ___ of the circle.

Area

If the radius of a circle is doubled, how does that affect the area of a sector given a constant angle?

The area of the sector becomes four times larger.

A sector with a radius of 8 cm and an angle of 90° has an area of ___.

32 cm²

True or False: The angle of a sector can be calculated as 360° minus the angle of the segment.

True