Arc Length and Area Sector

Front

What is the formula for the circumference of a circle?

Back

C = 2πr, where C is the circumference and r is the radius.

Front

How do you calculate the length of an arc?

Back

Arc Length = (θ/360) * C, where θ is the central angle in degrees and C is the circumference.

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 7 inches, what is the circumference?

Back

C = 2π(7) ≈ 43.98 inches.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

If the central angle of a sector is 90 degrees, what fraction of the circle does it represent?

Back

1/4 of the circle.

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 = π(5)² ≈ 78.54 square inches.

Front

If an arc measures 60 degrees in a circle with a radius of 10 cm, what is the length of the arc?

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 cm and a central angle of 45 degrees?

Back

Area = (45/360) * π(4)² = (1/8) * (16π) ≈ 6.28 cm².