What is the Circumference of a Circle?
A circle is a closed round shape where all the points on the boundary are equally spaced from a fixed point known as the center. The circumference of the circle is the total length of its boundary. Since it is a linear value, the circumference of a circle is generally measured in inches, meters, feet, and yards.
How to Calculate the Circumference of a Circle?
Since circles do not have straight edges like polygons, we cannot measure their boundary length with a ruler. We can find the circumference of a circle by knowing its radius or diameter. The radius of a circle is the distance between the center to any point on the circumference. The diameter of a circle is a line that passes through the center and meets the circumference at both ends. The diameter of a circle is twice the radius. The product of the constant value and the diameter of the circle gives the circumference.
Circumference of a circle, C = 2\(\pi r\)
or
Circumference of a circle, C = \(\pi\)d
The terms ‘r’ and ‘d’ indicate the radius and diameter of a circle.
Also, \(\pi\)(Pi) is the ratio of a circumference of a circle to its diameter. The value of Pi is 3.14 or \(\frac{22}{7}\).
Rapid Recall
Solved Examples on Diameter of a Circle
Example 1: If the radius of a circle is 30 cm, find its circumference.
Solution:
r = 30 cm
Use the formula to find the circumference of a circle:
C = 2\(\pi r\) [Write the formula]
= 2 x 3.14 x 30 [Substitute the value of r and \(\pi\)]
= 6.28 x 30
= 188.4
Therefore, the circumference of the given circle is 188.4 centimeters.
Example 2: Lisa got a brand new watch as her birthday present. What will be the length of its diameter if the circumference of the watch face is 26 millimeters?
Solution:
C = 26 mm
Use the circumference formula to calculate the diameter of the circle.
C = \(\pi\)d [Write the formula]
26 = 3.14 x d [Substitute the values]
\(\frac{26}{3.14}\) = d [Divide each side by 3.14]
8.28025 = d [Simplify]
Hence, the diameter of the watch face is 8.28 millimeters.
Example 3: If the circumference of a center circle on a soccer field is 63 yards, what is the radius of the center circle?
Solution:
Circumference of the center circle, C = 63 yards
We can find the radius using the following formula:
C = 2𝝿r [Write the formula]
63 = 2 x 3.14 x r [Substitute the values]
63 = 6.28 x r [Multiply]
\(\frac{63}{6.28}\) = r [Divide each side by 6.28]
r \(\approx\) 10
Therefore, the radius of the center circle is approximately 10 yards.
Pi is a constant value that is commonly used in geometry. The numerical value of pi is 3.14 or 22/7.
A chord that passes through the center of a circle is known as the diameter of the circle. But the circumference of a circle is the total length of its boundary.
The circumference is a one-dimensional linear quantity that can be expressed in meters, inches, centimeters, yards, and feet. It includes other units of length as well.
The circumference of a circle can be calculated by multiplying the diameter by a constant value pi.