Arc Length & Sector Area of Circles

Front

What is the formula for calculating the arc length of a circle?

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

How do you find the area of a sector in a circle?

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

What is the relationship between the angle of a sector and the arc length?

Back

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

Tags

CCSS.HSG.C.B.5

Front

If a circle has a radius of 10 inches, what is the arc length of a 90° sector?

Back

Arc Length = (90/360) * 2π(10) = 5π inches.

Tags

CCSS.HSG.C.B.5

Front

What is the area of a circle with a radius of 8 inches?

Back

Area = πr² = π(8)² = 64π square inches.

Tags

CCSS.7.G.B.4

Front

How do you convert an angle from radians to degrees?

Back

Multiply the angle in radians by (180/π).

Tags

CCSS.HSF.TF.A.1

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4

Front

If the area of a sector is 32π square inches and the angle is 60°, what is the radius?

Back

Radius = √(Area * (360/θ) / π) = √(32π * (360/60) / π) = 16 inches.

Tags

CCSS.HSG.C.B.5

Front

What is the formula for finding the angle of a sector given the arc length and radius?

Back

θ = (Arc Length / (2πr)) * 360.

Tags

CCSS.HSG.C.B.5

Front

How do you find the radius of a circle if you know the arc length and the angle?

Back

Radius = (Arc Length * 360) / (2πθ).

Tags

CCSS.HSG.C.B.5