Arc Length and Sector Area

Front

What is the formula for the area of a sector in a circle?

Back

Area = (θ/360) * π * r², where θ is the angle in degrees and r is the radius.

Front

How do you calculate the arc length of a sector?

Back

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

Front

What is 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 relationship between the radius and the area of a sector?

Back

The area of a sector increases with the square of the radius.

Front

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

Back

It represents 1/4 of the circle.

Front

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

Back

Area = (90/360) * π * (8)² = 16π in².

Front

What is the circumference of a circle with a radius of 10 in?

Back

Circumference = 2 * π * r = 20π in.

Front

If the area of a sector is 32π in² and the angle is 90°, what is the radius?

Back

Radius = √(Area * (360/θ) / π) = √(32π * (360/90) / π) = 16 in.

Front

What is an arc in a circle?

Back

An arc is a part of the circumference of a circle.

Front

How do you find the area of a sector with a radius of 5 m and an angle of 60°?

Back

Area = (60/360) * π * (5)² = (1/6) * 25π = (25/6)π m².