Sector Area and Arc Length

Front

What is the formula for the area of a sector?

Back

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

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

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 relationship between degrees and radians in a circle?

Back

A full circle is 360 degrees or 2π radians.

Front

If the radius of a circle is 6 inches and the central angle is 100°, what is the area of the shaded sector?

Back

Area = (100/360) * π * 6² ≈ 31.4 square inches.

Front

What is the area of a sector with a radius of 5 cm and a central angle of 90°?

Back

Area = (90/360) * π * 5² = (1/4) * π * 25 = 19.63 cm².

Front

How do you find the arc length of a circle with a radius of 10 cm and a central angle of 60°?

Back

Arc Length = (60/360) * 2π * 10 = (1/6) * 20π ≈ 10.47 cm.

Front

What is the area of a sector with a radius of 4 m and a central angle of 45°?

Back

Area = (45/360) * π * 4² = (1/8) * 16π = 6.28 m².

Front

If the radius of a circle is 8 cm and the central angle is 120°, what is the arc length?

Back

Arc Length = (120/360) * 2π * 8 = (1/3) * 16π ≈ 16.76 cm.

Front

What is the area of a sector with a radius of 3 inches and a central angle of 30°?

Back

Area = (30/360) * π * 3² = (1/12) * 9π ≈ 2.36 square inches.