Circles - Arc length and area of sectors + review

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the arc length of a circle?

Back

Arc Length = (θ/360) × 2πr, where θ is the central 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 for a given angle.

Front

Define 'arc length'.

Back

The distance along the curved line of a circle between two points.

Front

What is a sector of a circle?

Back

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

Front

If the radius of a circle is 5 units and the central angle is 60°, what is the area of the sector?

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.1 square units.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

If the arc length is 10 units and the radius is 4 units, what is the central angle in degrees?

Back

θ = (arc length / (2πr)) × 360 = (10 / (2π(4))) × 360 ≈ 143.2°.

Front

What is the area of a circle with a radius of 3 units?

Back

Area = πr² = π(3)² = 9π ≈ 28.3 square units.

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.