What is the formula for the circumference of a circle?

What is the formula for the circumference of a circle?

• A. C = \(\pi r^2\)
• B. C = \(2\pi r\)
• C. C = \( r^2 \pi^2\)
• D. C = \(\frac{1}{2} \pi r\)

Answer: (B)

The formula for the circumference of a circle is indeed represented as \(C = 2\pi r\), where \(C\) represents the circumference and \(r\) is the radius of the circle. This formula emerges from the relationship between the diameter and the radius, as the diameter of a circle is twice the radius (i.e., \(d = 2r\)). Since the circumference is the distance around the circle, it can also be expressed in terms of the diameter: \(C = \pi d\). By substituting \(d\) with \(2r\), we arrive at the formula \(C = 2\pi r\). This equation illustrates that the circumference is directly proportional to the radius, meaning that as the radius increases, the circumference also increases in a linear manner, multiplied by the constant \(\pi\). Understanding this formula is fundamental in geometry and is frequently used in various applications, including physics, engineering, and everyday calculations involving circular objects.

The formula for the circumference of a circle is indeed represented as (C = 2\pi r), where (C) represents the circumference and (r) is the radius of the circle. This formula emerges from the relationship between the diameter and the radius, as the diameter of a circle is twice the radius (i.e., (d = 2r)). Since the circumference is the distance around the circle, it can also be expressed in terms of the diameter: (C = \pi d). By substituting (d) with (2r), we arrive at the formula (C = 2\pi r).

This equation illustrates that the circumference is directly proportional to the radius, meaning that as the radius increases, the circumference also increases in a linear manner, multiplied by the constant (\pi). Understanding this formula is fundamental in geometry and is frequently used in various applications, including physics, engineering, and everyday calculations involving circular objects.