Arc Length & Sector Area

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

What is the formula for the area of a sector?

Back

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

Tags

CCSS.HSG.C.B.5

Front

Define 'radian' in the context of angles.

Back

A radian is the angle formed when the arc length is equal to the radius of the circle.

Tags

CCSS.HSG.CO.C.9

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Tags

CCSS.HSF.TF.A.1

Front

What is the relationship between arc length and radius?

Back

Arc Length is directly proportional to the radius; as the radius increases, the arc length increases.

Tags

CCSS.HSG.C.B.5

Front

What is the area of a full circle?

Back

Area = πr².

Tags

CCSS.7.G.B.4

Front

If the radius of a circle is 5 cm, what is the area of a sector with a central angle of 90 degrees?

Back

Area of Sector = (90/360) * π(5)² = (1/4) * 25π = 6.25π cm².

Tags

CCSS.HSG.C.B.5

Front

What is the circumference of a circle?

Back

Circumference = 2πr.

Tags

CCSS.7.G.B.4

Front

How do you find the central angle given the arc length and radius?

Back

θ = (Arc Length / r) * (180/π).

Tags

CCSS.HSG.C.B.5

Front

What is the area of a sector with a radius of 10 m and a central angle of 60 degrees?

Back

Area of Sector = (60/360) * π(10)² = (1/6) * 100π = 16.67π m².

Tags

CCSS.HSG.C.B.5