Geometry Arc Length

Front

What is the formula for arc length in a circle?

Back

The arc length (L) can be calculated using the formula: L = r * θ, where r is the radius and θ is the angle in radians.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: radians = degrees * (π/180).

Front

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

Back

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

Front

If the radius of a circle is 5 feet and the angle is 60 degrees, what is the arc length?

Back

First convert 60 degrees to radians: 60 * (π/180) = π/3. Then, use the formula: L = r * θ = 5 * (π/3) = (5π/3) feet.

Front

What is the arc length of a semicircle with a radius of 10 feet?

Back

The angle for a semicircle is 180 degrees or π radians. Using the formula: L = r * θ = 10 * π = 10π feet.

Front

Define 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 area of a sector with radius r and angle θ in radians?

Back

The area (A) of a sector can be calculated using the formula: A = (1/2) * r^2 * θ.

Front

How do you find the length of an arc given the radius and the angle in degrees?

Back

Convert the angle from degrees to radians and then use the arc length formula: L = r * θ.

Front

What is the arc length of a circle with a radius of 8 feet and an angle of 90 degrees?

Back

Convert 90 degrees to radians: 90 * (π/180) = π/2. Then, L = 8 * (π/2) = 4π feet.

Front

If an arc length is 12π feet and the radius is 6 feet, what is the angle in degrees?

Back

Using the formula L = r * θ, we have 12π = 6 * θ. Thus, θ = 12π/6 = 2π radians, which is 360 degrees.