Arc Length and Sector Area

Front

What is the formula for calculating the arc length of a circle?

Back

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

Front

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

Back

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

Front

If a circle has a radius of 10 feet and a central angle of 90 degrees, what is the length of the arc?

Back

Arc Length = (90/360) × 2π(10) = 15.7 feet.

Front

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

Back

Diameter = 2 × Radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the circumference of a circle with a radius of 7 feet?

Back

Circumference = 2π(7) = 43.98 feet.

Front

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

Back

Area = π(5)² = 78.54 in².

Front

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

Back

The area increases by a factor of 4.

Front

What is the arc length of a circle with a radius of 12 feet and a central angle of 180 degrees?

Back

Arc Length = (180/360) × 2π(12) = 37.7 feet.

Front

What is the area of a sector with a radius of 8 inches and a central angle of 45 degrees?

Back

Area of Sector = (45/360) × π(8)² = 11.3 in².