RPA 9x1 Sectors and arc length

Front

What is the formula for arc length?

Back

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

Front

Define 'sector' in the context of a circle.

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

What is the formula for the area of a sector?

Back

Area of a Sector = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the relationship between arc length and radius?

Back

Arc length increases with an increase in radius for a given central angle.

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 measure of a full circle in degrees?

Back

360 degrees.

Front

What is the measure of a full circle in radians?

Back

2π radians.

Front

If the central angle of a sector is 90 degrees, what fraction of the circle does it represent?

Back

1/4 of the circle.

Front

What is the length of an arc with a radius of 5 feet and a central angle of 60 degrees?

Back

Arc Length = (60/360) * 2π(5) = (1/6) * 10π = 5π/3 feet.