Arc Length and Sector Area

Front

What is an arc?

Back

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

Tags

CCSS.HSG.C.B.5

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.

Tags

CCSS.HSG.C.B.5

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.

Tags

CCSS.HSG.C.B.5

Front

What is the circumference of a circle?

Back

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

Tags

CCSS.7.G.B.4

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.

Tags

CCSS.HSG.C.A.2

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.

Tags

CCSS.7.G.B.4

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.

Tags

CCSS.HSG.C.B.5

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.

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

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.

Tags

CCSS.HSG.C.B.5