Arc Length & Area Of Sectors Review

Front

What is the formula for arc length in a circle?

Back

The formula for arc length (L) is given by: L = r * θ, where r is the radius and θ is the central 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 formula for the area of a sector in a circle?

Back

The area (A) of a sector is given by: A = (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians.

Front

If a circle has a radius of 5 cm, what is the circumference?

Back

The circumference (C) is given by: C = 2 * π * r = 2 * π * 5 = 10π cm.

Front

What is the relationship between arc length and the radius of a circle?

Back

Arc length is directly proportional to both the radius and the central angle of the circle.

Front

How do you find the central angle if you know the arc length and radius?

Back

Use the formula: θ = L/r, where L is the arc length and r is the radius.

Front

What is the area of a circle with a radius of 7 cm?

Back

The area (A) is given by: A = π * r^2 = π * 7^2 = 49π cm².

Front

If the area of a sector is 12π cm² and the radius is 4 cm, what is the central angle in degrees?

Back

First, find θ using A = (1/2) * r^2 * θ: 12π = (1/2) * 4^2 * θ. Solving gives θ = 6 radians, which is 6 * (180/π) = 343.77°.

Front

What is the formula to find the area of a segment in a circle?

Back

Area of a segment = Area of the sector - Area of the triangle formed by the radius and the chord.

Front

If an arc length is 10 cm and the radius is 5 cm, what is the central angle in radians?

Back

Using θ = L/r, θ = 10/5 = 2 radians.