Sector Area and Arc Length

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) × πr², where θ is the angle in degrees and r is the radius.

Front

What is the formula for the length of an arc?

Back

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

Front

Define a sector of a circle.

Back

A region bounded by two radii of the circle and their intercepted arc.

Front

What is the relationship between arc length and the circumference of a circle?

Back

Arc Length is proportional to the circumference of a circle.

Front

If the radius of a circle is 10 inches and the angle is 90°, what is the area of the sector?

Back

Area = (90/360) × π(10)² = 25π in².

Front

If an arc has a length of 15 cm and the radius is 5 cm, what is the angle in degrees?

Back

θ = (Arc Length / (2πr)) × 360 = (15 / (2π(5))) × 360 = 171.89°.

Front

What is the total area of a circle with a radius of 7 inches?

Back

Total Area = πr² = π(7)² = 49π in².

Front

How do you find the radius if you know the arc length and the angle?

Back

Radius = (Arc Length × 360) / (2πθ).

Front

What is the circumference of a circle with a radius of 4 meters?

Back

Circumference = 2πr = 2π(4) = 8π meters.

Front

If the area of a sector is 20 in² and the radius is 5 in, what is the angle?

Back

θ = (Area × 360) / (πr²) = (20 × 360) / (π(5)²) = 144°.