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 angle in degrees and r is the radius.

Front

How do you calculate the arc length of a sector?

Back

Arc Length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.

Front

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

Back

The area of a sector is directly proportional to the angle of the sector.

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 unit of measurement for area in the context of sectors?

Back

Square units (e.g., cm², m², yd²).

Front

What is the unit of measurement for arc length?

Back

Linear units (e.g., cm, m, yd).

Front

If a sector has an angle of 90 degrees, what fraction of the circle does it represent?

Back

It represents 1/4 of the circle.

Front

Calculate the area of a sector with a radius of 5 cm and an angle of 60 degrees.

Back

Area = (60/360) × π(5)² = 13.09 cm².

Front

Calculate the arc length of a sector with a radius of 10 m and an angle of 120 degrees.

Back

Arc Length = (120/360) × 2π(10) = 20.94 m.

Front

What is the area of a sector with a radius of 7 yd and an angle of 180 degrees?

Back

Area = (180/360) × π(7)² = 38.48 yd².