Circle Length of Arc and Area of Sector

Front

What is the formula for the length of an arc in a circle?

Back

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

Front

How do you calculate 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.

Front

What is the relationship between the angle in radians and the length of an arc?

Back

Length of Arc = r * θ, where θ is the angle in radians.

Front

If the radius of a circle is doubled, how does the length of the arc change?

Back

The length of the arc also doubles, since it is directly proportional to the radius.

Front

What is the area of a full circle with radius r?

Back

Area = πr².

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the measure of a full circle in radians?

Back

2π radians.

Front

If a sector has an angle of 90°, what fraction of the circle does it represent?

Back

1/4 of the circle.

Front

What is the area of a sector with a radius of 8 cm and an angle of 90°?

Back

Area = (90/360) * π * 8² = 16π cm².

Front

How do you find the radius if you know the area of a sector and the angle?

Back

Rearrange the area formula: r = √(Area * (360/θ) / π).