arc length and sector area

Front

What is the formula for arc length in a circle?

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 in a circle?

Back

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

Front

What is the relationship between the radius and diameter of a circle?

Back

Diameter = 2 * Radius.

Front

If the radius of a circle is 10 inches, what is the circumference?

Back

Circumference = 2πr = 2π(10) = 20π inches.

Front

What is the central angle of a full circle in degrees?

Back

360 degrees.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

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

Back

Area = πr² = π(5)² = 25π square inches.

Front

If a sector has a central angle of 90 degrees and a radius of 4 inches, what is the area of the sector?

Back

Area = (90/360) * π(4)² = (1/4) * 16π = 4π square inches.

Front

What is the length of an arc with a radius of 12 feet and a central angle of 60 degrees?

Back

Arc Length = (60/360) * 2π(12) = (1/6) * 24π = 4π feet.

Front

What is the formula to find the area of a sector if the angle is in radians?

Back

Area of Sector = (1/2) * r² * θ, where θ is in radians.