Section 5-3: Arc Length & Sector Area

Front

What is the formula for the length of an arc?

Back

The length of an arc (L) can be calculated using the formula: L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

How do you calculate the area of a sector?

Back

The area of a sector (A) can be calculated using the formula: A = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

What is a minor arc?

Back

A minor arc is an arc that is smaller than a semicircle, measuring less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that is larger than a semicircle, measuring more than 180 degrees.

Front

If the radius of a circle is 10 cm, what is the area of a sector with a central angle of 60 degrees?

Back

A = (60/360) * π(10)² = (1/6) * 100π = 16.67 cm² (approximately).

Front

What is the relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle; as the angle increases, the arc length increases.

Front

How do you find the measure of a minor arc given the distance traveled along the circumference?

Back

Use the formula: θ = (L / (2πr)) * 360, where L is the distance traveled and r is the radius.

Front

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

Back

The area of the circle is A = πr² = π(5)² = 25π m².

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) can be calculated using the formula: C = 2πr, where r is the radius.

Front

If a circle has a radius of 7 inches, what is the length of a minor arc that subtends a central angle of 45 degrees?

Back

L = (45/360) * 2π(7) = (1/8) * 14π = 5.5 inches (approximately).