Area of Sector

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

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 cm and a central angle of 60°?

Back

Area = (60/360) × π(5)² = 13.09 cm² (rounded to 2 decimal places).

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 4, since area is proportional to the square of the radius.

Front

What is the relationship between the central angle and the area of a sector?

Back

The area of a sector is directly proportional to the central angle; as the angle increases, the area increases.

Front

Find the area of a sector with a radius of 10 inches and a central angle of 90°.

Back

Area = (90/360) × π(10)² = 78.54 in² (rounded to 2 decimal places).

Front

What is the area of a sector with a radius of 8 cm and a central angle of 45°?

Back

Area = (45/360) × π(8)² = 11.30 cm² (rounded to 2 decimal places).

Front

How do you find the area of a shaded sector in a circle?

Back

Use the formula Area = (θ/360) × πr², where θ is the angle of the shaded sector.

Front

What is the area of a sector with a radius of 12 cm and a central angle of 120°?

Back

Area = (120/360) × π(12)² = 50.27 cm² (rounded to 2 decimal places).

Front

If a sector has an area of 25 cm² and a radius of 5 cm, what is the central angle?

Back

θ = (Area × 360) / (πr²) = (25 × 360) / (π(5)²) = 72°.