Diameter Formula
Before we begin with the diameter formula, let us recall what is a diameter. Diameter is one of the important parts of a circle. The straight line connecting a point from one end of the circle to a point on the other end of the circle and passing through the center is called a diameter. Since there are infinite points on its circumference, this means that a circle has an infinite number of diameters and each diameter of the circle has an equal length.
Let us learn the Diameter Formula with a few solved examples.
Formula to Find Diameter
We can find the diameter of a circle when the radius, area, or circumference is known.
Formula 1: The diameter is twice the length of the radius.
\[\text{Diameter} = 2 \times \text{Radius}\]
Formula 2: The diameter is the ratio of circumference to \(\pi\).
\[\text{Diameter} = \frac{\text{Circumference}}{\pi}\]
Formula 3: We can derive the diameter formuls using the area formula which is \(\text{Area} = \pi (\text{Radius})^2\).
\[\text{Diameter} = 2 \sqrt{\frac{\text{Area}}{\pi}}\]
Solved Examples on Diameter Formula
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Example 1:
Find the diameter of a circle whose radius is 24 inches long.
Solution:
We will use the first formula to find the Diameter of the circle.
\(\begin{align}\text{Diameter} &= 2 \times \text{Radius}\\&=2 \times 24 \text{ inches}\\&=48 \text{ inches}\end{align}\)Answer: Diameter of the given circle = 48 inches.
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Example 2:
Find the diameter of a circle whose circumference is \(4\pi\) units.
Solution:
We will use the second formula to find the Diameter of the circle.
\(\begin{align}\text{Diameter} &= \frac{\text{Circumference}}{\pi}\\&=\frac{4\pi \text{ units}}{\pi}\\&=4 \text{ units}\end{align}\)Answer: Diameter of the given circle = 4 units.