Circles - Area of Sector (Hoover)

Front

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

Back

Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

Front

How do you find the central angle of a sector if you know the arc length and radius?

Back

Central angle (θ) = (arc length / radius) * (180/π).

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

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

Back

The area of the sector increases by a factor of four.

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 * 5² = (1/4) * π * 25 = 6.25π square inches.

Front

How do you convert degrees to radians for calculating the area of a sector?

Back

Radians = degrees * (π/180).

Front

What is the area of a sector with a radius of 10 cm and a central angle of 60°?

Back

Area = (60/360) * π * 10² = (1/6) * π * 100 = 16.67π cm².

Front

What is the area of a sector with a radius of 8 units and a central angle of 120°?

Back

Area = (120/360) * π * 8² = (1/3) * π * 64 = 21.33π square units.

Front

How do you find the area of a sector if the arc length is known?

Back

Area = (arc length * radius) / 2.

Front

What is the area of a sector with a radius of 3 meters and an arc length of 4.71 meters?

Back

Area = (4.71 * 3) / 2 = 7.065 square meters.