April 16th Flashcardziz Arc Length and Sector Area

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) * π * r², where θ is the angle in degrees and r is the radius.

Front

How do you calculate the arc length of a circle?

Back

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

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

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 value of π (pi)?

Back

π is approximately 3.14, but it is an irrational number that continues infinitely.

Front

How do you convert degrees to radians?

Back

Radians = Degrees * (π/180).

Front

What is the area of a circle?

Back

Area = π * r², where r is the radius.

Front

If the radius of a circle is doubled, how does the area change?

Back

The area increases by a factor of four, since Area = π * (2r)² = 4π * r².

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2 * π * r, where r is the radius.

Front

How do you find the central angle of a sector given the area?

Back

Central Angle (θ) = (Area of Sector / Area of Circle) * 360.