Arc Length and Sector Area

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

What is the formula for 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

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the arc length?

Back

Arc Length = (60/360) * 2π(10) = 10.47 cm.

Front

If the radius of a circle is 5 units and the central angle is 90 degrees, what is the area of the sector?

Back

Area of Sector = (90/360) * π(5)² = 19.63 units².

Front

What is the relationship between the radius and the arc length?

Back

The arc length increases linearly with the radius for a given central angle.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the circumference of a circle with a radius of 7 cm?

Back

Circumference = 2πr = 2π(7) = 43.98 cm.

Front

If the arc length is 12.8 ft and the radius is 4 ft, what is the central angle in degrees?

Back

θ = (Arc Length / (2πr)) * 360 = (12.8 / (2π(4))) * 360 = 60 degrees.

Front

What is the area of a circle with a radius of 3 cm?

Back

Area = πr² = π(3)² = 28.27 cm².

Front

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

Back

The arc length also doubles for the same central angle.