Question

How do you find diameter from the circumference of a circle?

Answer 1

Step 1: Define the diameter and the circumference of a circle:

The diameter is the longest chord of a circle that passes through the center. The diameter of a circle is double its radius, i.e., $D=2r$.

The perimeter of a circle is called the circumference of a circle. It is defined by the formula $C=2\mathrm{\pi r}$.

Step 2: Calculate the diameter from the circumference

Since, $D=2r$

$\Rightarrow$ $r=\frac{D}{2}$ …(i)

Now, if it is known that $C=2\mathrm{\pi r}$ …(ii)

Using equation (i) in the equation (ii), we get,

$C=2\pi \times \frac{D}{2}$

$\Rightarrow C=\pi \times D$

$$\begin{gathered} \Rightarrow C=\pi D \\ \Rightarrow D=\frac{\mathrm{\pi }}{\mathrm{C}} \end{gathered}$$

the above formula can be used to calculate diameter if the circumference is known.

Hence, the diameter from the circumference of a circle can be calculated using the formula $D=\frac{\pi }{C}$.