1st Applying Arc Length & Sector Area

Front

What is the formula for the area of a sector in a circle?

Back

Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

Front

How do you calculate the arc length of a sector?

Back

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

Front

What is the relationship between radians and degrees?

Back

1 radian = 180/π degrees.

Front

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

Back

Circumference = 2 * π * r = 2 * π * 10 = 20π inches.

Front

What is the formula for the area of a circle?

Back

Area = π * r², where r is the radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees * (π/180).

Front

What is the central angle of a sector if the arc length is equal to the radius?

Back

The central angle is 1 radian.

Front

If a sector has an area of 50π in² and a central angle of 60°, what is the radius?

Back

Radius = √(Area / (θ/360 * π)) = √(50π / (60/360 * π)) = 10 inches.

Front

What is the formula for finding the diameter of a circle from the arc length and central angle in radians?

Back

Diameter = (Arc Length / θ) * 2.

Front

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

Back

The area increases by a factor of 4 (Area = π * (2r)² = 4π * r²).