Arc Length and Sector Area

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 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 10 inches and the central angle is 90 degrees, what is the arc length?

Back

Arc Length = (90/360) * 2π(10) = 15.71 inches.

Front

If the radius of a circle is 5 feet and the central angle is 60 degrees, what is the area of the sector?

Back

Area of Sector = (60/360) * π(5)² = 13.09 square feet.

Front

What is the relationship between the radius and the arc length?

Back

The arc length increases as the radius increases, given a constant central angle.

Front

How does the central angle affect the area of a sector?

Back

The area of a sector increases as the central angle increases, given a constant radius.

Front

What is the arc length of a circle with a radius of 7 cm and a central angle of 120 degrees?

Back

Arc Length = (120/360) * 2π(7) = 14.66 cm.

Front

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

Back

Area of Sector = (45/360) * π(8)² = 11.18 square meters.

Front

If the arc length is 10 m and the radius is 5 m, what is the central angle in degrees?

Back

θ = (Arc Length / (2πr)) * 360 = (10 / (2π(5))) * 360 = 114.59 degrees.

Front

What is the area of a sector with a radius of 12 inches and a central angle of 30 degrees?

Back

Area of Sector = (30/360) * π(12)² = 12.57 square inches.