Unit 10: Circles - Homework 3: Arc Lengths

Front

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

Back

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

Front

If the radius of a circle is 10 m, what is the length of an arc that subtends a central angle of 60 degrees?

Back

Arc Length = (60/360) * 2π(10) = 10.47 m.

Front

Define 'central angle' in the context of circles.

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 circumference.

Front

What is the relationship between the diameter and radius of a circle?

Back

The radius is half of the diameter. r = d/2.

Front

If a circle has a diameter of 20 cm, what is its radius?

Back

Radius = 20 cm / 2 = 10 cm.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the circumference of a circle with a radius of 5 m?

Back

Circumference = 2πr = 2π(5) = 31.42 m.

Front

If a Ferris wheel has a diameter of 225 feet, what is its radius?

Back

Radius = 225 ft / 2 = 112.5 ft.

Front

What is the formula for calculating the angle of rotation based on arc length?

Back

θ = (Arc Length / Radius) × (180/π).

Front

If a passenger travels 38 feet on a Ferris wheel with a radius of 112.5 feet, what is the angle of rotation?

Back

θ = (38 / 112.5) × (180/π) ≈ 19°.