Arc Length and Circumference

Front

What is the formula for the circumference of a circle?

Back

C = πd or C = 2πr, where d is the diameter and r is the radius.

Front

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

Back

Arc length (L) can be calculated using the formula L = (θ/360) * C, where θ is the central angle in degrees and C is the circumference.

Front

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

Back

The diameter (d) is twice the radius (r): d = 2r.

Front

What is the area of a circle?

Back

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

Front

If the diameter of a circle is 16.4 m, what is the radius?

Back

The radius is half of the diameter: r = 16.4 m / 2 = 8.2 m.

Front

How do you express the length of an arc in terms of pi?

Back

To express the length of an arc in terms of pi, calculate the arc length using the formula and leave the answer in terms of π.

Front

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

Back

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

Front

What is the significance of leaving answers in terms of pi?

Back

Leaving answers in terms of pi provides an exact value rather than a decimal approximation.

Front

How do you convert the circumference of a circle to the length of an arc?

Back

To find the length of an arc, multiply the circumference by the fraction of the circle represented by the arc's central angle.

Front

What is the central angle of a circle?

Back

The central angle is the angle whose vertex is at the center of the circle and whose sides intersect the circle.