Circles Review

Front

What is a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides (rays) intersect the circle at two points.

Front

How do you calculate the length of an arc in a circle?

Back

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

Front

What is the relationship between a central angle and its intercepted arc?

Back

The measure of a central angle is equal to the measure of its intercepted arc.

Front

If the radius of a circle is 24 feet and the central angle is 165 degrees, what is the length of the arc?

Back

Using the formula: Arc Length = (165/360) * 2π(24) ≈ 69 feet.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula: C = 2πr, where r is the radius.

Front

What is the measure of a full circle in degrees?

Back

A full circle measures 360 degrees.

Front

How do you find the area of a sector of a circle?

Back

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

Front

What is the difference between a minor arc and a major arc?

Back

A minor arc is the shorter arc connecting two points on a circle, while a major arc is the longer arc connecting the same two points.

Front

If the length of an arc is 49.7 ft, what could be the radius if the central angle is 90 degrees?

Back

Using the formula: Arc Length = (90/360) * 2πr, we can solve for r: r ≈ 31.6 ft.

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula: A = πr², where r is the radius.