Arc Length and Sector Area

Front

What is the formula for arc length?

Back

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

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

Define 'central angle' in a circle.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circle.

Front

What is the relationship between the radius and the arc length?

Back

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

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the area of a circle?

Back

Area = πr², where r is the radius of the circle.

Front

If the radius of a circle is 10 inches and the central angle is 90°, what is the area of the sector?

Back

Area of Sector = (90/360) * π(10)² = 25π ≈ 78.54 square inches.

Front

What is the length of an arc with a radius of 5 cm and a central angle of 60°?

Back

Arc Length = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.

Front

What is the significance of the central angle in determining the area of a sector?

Back

The central angle determines the fraction of the circle's area that the sector occupies.

Front

How do you find the area of a shaded region in a circle?

Back

Subtract the area of the unshaded part from the total area of the circle.