Arc Length and Area Sector

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

How do you calculate the area of a sector?

Back

Area of Sector = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

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

Back

The arc length also doubles.

Front

What is the area of a circle with a radius of 5 cm?

Back

Area = π(5)² = 25π cm².

Front

What is the relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle.

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 10 cm and a central angle of 90°?

Back

Area = (90/360) * π(10)² = 25π cm².

Front

What is the arc length of a circle with a radius of 4 cm and a central angle of 60°?

Back

Arc Length = (60/360) * 2π(4) = (1/6) * 8π = (4/3)π cm.

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 = (1/8) * 64π = 8π cm².