Arc Length & Sector Area

Front

What is the formula for arc length in a circle?

Back

Arc Length = (θ/360) * 2πr, 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 area of a sector in a circle?

Back

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

Tags

CCSS.HSG.C.B.5

Front

If the radius of a circle is 10 inches and the central angle is 90°, what is the arc length?

Back

Arc Length = (90/360) * 2π(10) = 15.7 inches.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between arc length and radius?

Back

Arc length increases with an increase in radius for a given central angle.

Tags

CCSS.HSG.C.B.5

Front

Define a sector in a circle.

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

What is the central angle of a full circle?

Back

The central angle of a full circle is 360°.

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

Front

If the arc length is 20 cm and the radius is 5 cm, what is the central angle in degrees?

Back

θ = (Arc Length / (2πr)) * 360 = (20 / (2π(5))) * 360 = 144°.

Tags

CCSS.HSG.C.B.5

Front

What is the area of a sector with a radius of 4 cm and a central angle of 60°?

Back

Area = (60/360) * π(4)² = (1/6) * 16π = 8.4 cm².

Tags

CCSS.HSG.C.B.5

Front

How do you convert radians to degrees?

Back

Degrees = Radians * (180/π).

Tags

CCSS.HSF.TF.A.1

Front

What is the formula for finding the radius if the arc length and central angle are known?

Back

Radius = (Arc Length * 360) / (2πθ).

Tags

CCSS.HSG.C.B.5