Arc Length and Area of Sector

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the length of an arc?

Back

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

Front

What is the area of a sector with a radius of 6 inches and a central angle of 100°?

Back

31.4 sq. in.

Front

If the radius of a circle is 24 feet and the angle is 165°, what is the length of the arc?

Back

69 feet.

Front

What is the area of a sector with a radius of 10 inches and a central angle of 60°?

Back

Area = (60/360) × π(10)² = 52.4 in².

Front

Define 'sector' in the context of 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 central angle and the area of a sector?

Back

The area of a sector is directly proportional to the central angle.

Front

How do you express the area of a sector in terms of radians?

Back

Area = (1/2) × r² × θ, where θ is in radians.

Front

What is the area of a sector with a radius of 5 inches and a central angle of 90°?

Back

Area = (90/360) × π(5)² = 19.63 in².

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr.