Arc Length and Area Sector

Front

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

Back

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

Front

Define a sector 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 formula for the area of a sector?

Back

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

Front

How do you find the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

If the radius of a circle is 6 inches, what is the circumference?

Back

Circumference = 2π(6) ≈ 37.7 inches.

Front

What is the relationship between the central angle and the arc length?

Back

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

Front

Calculate the arc length for a circle with a radius of 10 cm and a central angle of 90 degrees.

Back

Arc Length = (90/360) * 2π(10) = 15.7 cm.

Front

What is the area of a sector with a radius of 5 cm and a central angle of 60 degrees?

Back

Area = (60/360) * π(5)² ≈ 13.1 cm².

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the arc length of a circle with a radius of 8 m and a central angle of 45 degrees?

Back

Arc Length = (45/360) * 2π(8) ≈ 3.14 m.