Arc Length and Sector Area

Front

What is an arc?

Back

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

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the length of an arc?

Back

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

Front

What is the circumference of a circle?

Back

Circumference = 2πr, where r is the radius of the circle.

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii.

Front

If the radius of a circle is 10 inches, what is the circumference?

Back

Circumference = 2π(10) = 20π inches or approximately 62.83 inches.

Front

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

Back

The arc length is directly proportional to the central angle; as the angle increases, the arc length increases.

Front

What is a sector?

Back

A sector is a region of a circle bounded by two radii and the arc between them.

Front

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

Back

It represents 1/4 of the circle.

Front

What is the area of a sector with a radius of 5 inches and a central angle of 60 degrees?

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.09 square inches.