Arc Length and Sector Area

Front

What is the term for the angle formed at the center of a circle by two radii?

Back

Central angle

Front

What is an arc?

Back

An arc is a smaller piece of the circumference of a circle.

Front

How do you calculate the area of a sector?

Back

Area of sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

What is the formula for finding the length of an arc?

Back

Length of arc = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Front

If the radius of a circle is 6 inches and the central angle is 100°, what is the area of the sector?

Back

31.4 sq. in.

Front

What is the relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle.

Front

What is the circumference of a circle with a radius of 7 cm?

Back

Circumference = 2πr = 2π(7) = 14π cm.

Front

If the central angle of a sector is 90°, what fraction of the circle does the sector represent?

Back

1/4 of the circle.

Front

What is the area of a circle with a radius of 5 cm?

Back

Area = πr² = π(5)² = 25π cm².

Front

How do you convert degrees to radians?

Back

Radians = degrees × (π/180).