Arc Length and Sector Area

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

What is the formula for the area of a sector?

Back

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

Front

Define 'arc' in the context of a circle.

Back

An arc is a portion of the circumference of a circle.

Front

What is the relationship between the radius and the arc length?

Back

The arc length increases with an increase in the radius, given a constant angle.

Front

How do you find the measure of an arc given the central angle?

Back

The measure of the arc in degrees is equal to the measure of the central angle.

Front

What is the difference between a chord and an arc?

Back

A chord is a line segment connecting two points on a circle, while an arc is the curved line between those two points.

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) = (1/6) × 20π = 10π cm.

Front

What is the circumference of a circle with a radius of 5 ft?

Back

Circumference = 2πr = 2π(5) = 10π ft.

Front

How do you calculate the area of a circle?

Back

Area = πr², where r is the radius.

Front

What is the area of a sector with a radius of 4 m and a central angle of 90 degrees?

Back

Area of Sector = (90/360) × π(4)² = (1/4) × 16π = 4π m².