Circles: Arc Length and Sector Area

Front

What is the formula for the area of a sector of a circle?

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 a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle.

Front

If the radius of a circle is 6 inches and the central angle is 100°, what is the area of the shaded sector?

Back

10π square inches.

Front

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

Back

The area of a sector increases with the square of the radius.

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.

Front

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

Back

The area increases by a factor of four.

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the area of a sector with a radius of 5 inches and a central angle of 90°?

Back

Area = (90/360) × π(5)² = (1/4) × 25π = 25π/4 square inches.