Arc Length and Circumference

Front

What is the formula for arc length?

Back

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

Front

Define circumference.

Back

Circumference is the distance around a circle, calculated as C = 2πr or C = πd, where r is the radius and d is the diameter.

Front

How do you find the radius if you know the circumference?

Back

Radius can be found using the formula r = C/(2π).

Front

What is the relationship between the angle and arc length in a circle?

Back

The arc length is directly proportional to the angle subtended at the center of the circle.

Front

If the radius of a circle is 5 cm, what is the circumference?

Back

C = 2π(5) = 10π ≈ 31.42 cm.

Front

What is the area of a sector with a radius of r and angle θ?

Back

Area = (θ/360) * πr².

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the arc length of a circle with a radius of 4 m and a central angle of 90 degrees?

Back

Arc Length = (90/360) * 2π(4) = 2π m ≈ 6.28 m.

Front

What is a minor arc?

Back

A minor arc is an arc that is smaller than a semicircle, subtended by an angle less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that is larger than a semicircle, subtended by an angle greater than 180 degrees.