Arc Length and Sector Area

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

What is the formula for the area of a sector?

Back

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

Front

Define 'arc length'.

Back

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

Front

Define 'sector area'.

Back

Sector area is the area enclosed by two radii of a circle and the arc between them.

Front

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the arc length?

Back

Arc Length = (60/360) × 2π(10) = 10.47 cm.

Front

If the radius of a circle is 5 cm and the central angle is 90 degrees, what is the area of the sector?

Back

Area of Sector = (90/360) × π(5)² = 19.63 cm².

Front

What is the relationship between the radius and arc length?

Back

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

Front

How does the central angle affect the arc length?

Back

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

Front

What is the arc length of a full circle?

Back

Arc Length of a full circle = 2πr.

Front

What is the area of a full circle?

Back

Area of a full circle = πr².