Arc Length and Sector Area

Front

What is the formula for arc length in a circle?

Back

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

Front

Define a sector of a circle.

Back

A sector of a circle is a region bounded by two radii and the arc between them.

Front

What is the relationship between the radius and the area of a sector?

Back

The area of a sector can be calculated using the formula: Area = (θ/360) * πr², where θ is the angle in degrees.

Front

How do you find the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

What is the measure of a full circle in degrees?

Back

A full circle measures 360 degrees.

Front

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

Back

The circumference also doubles, since it is directly proportional to the radius.

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.

Front

How do you calculate the area of a sector with a 90° angle and a radius of 8 units?

Back

Area = (90/360) * π * 8² = 16π square units.

Front

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

Back

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

Front

Define arc length.

Back

Arc length is the distance along the curved line of a circle between two points.