Arc Length and Sector Area

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

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

Define a sector in a circle.

Back

A sector is a portion of a circle enclosed 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 increases with the square of the radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is 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 central angle of a full circle in degrees?

Back

360 degrees.

Front

How do you find the area of a shaded sector given the angle and radius?

Back

Use the formula: Area = (θ/360) × πr².

Front

What is the arc length of a circle with a radius of 10 cm and a central angle of 90 degrees?

Back

Arc Length = (90/360) × 2π(10) = 15.71 cm.