Arc Length and Sector Area

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) × πr², where θ is the angle in degrees and r is the radius.

Front

What is the formula for arc length?

Back

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

Front

Define '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 relationship between the angle of a sector and its area?

Back

The area of a sector is directly proportional to the angle of the sector.

Front

How do you convert radians to degrees?

Back

Degrees = Radians × (180/π).

Front

What is the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

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

Back

The area of the sector increases by a factor of four.

Front

What is the area of a full circle?

Back

Area = πr², where r is the radius.

Front

How do you find the angle of a sector if you know the area and radius?

Back

θ = (Area × 360) / (πr²).

Front

What is the relationship between arc length and radius?

Back

Arc length increases linearly with the radius for a given angle.