Question

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

Answer 1

Hint: In the given question, we have been given to evaluate the value of diameter of any circle. We have been given that in the given scenario, we have the circumference of the circle. Using the value of the circumference, we have to calculate the diameter. To do that, we assume the circumference of the circle to be any variable. Then we write the standard formula of the circumference. Then we take out the diameter from the formula, keep it on that side and take the rest of the things to the other side. And that gives us the required relation.

Formula Used:
We are going to use the formula of circumference \[\left( c \right)\] of a circle whose radius is \[r\]:
\[c = 2\pi r\]

Complete step-by-step answer:
Let the given circumference be \[c\]. Let the diameter be \[d\].
First, let us write the formula of circumference:
We know,
\[c = 2\pi r\] …(i)
Now, let us write the relation between diameter and radius:
Also, we know that,
\[2r = d\] …(ii)
Now, let us compare equations (i) and (ii), we have,
\[c = \pi \times \left( {2r} \right) = \pi d\]
Thus, \[d = \dfrac{c}{\pi }\]

Additional Information:
We have to change the radius of the circle to diameter as we have to calculate the value of the diameter. The relation between radius and diameter is:
\[diameter = 2 \times radius\]

Note: In the given question, we had to formulate a relation to calculate the diameter of any circle whose circumference is given. To do that, we assumed the circumference to be any variable. Then we wrote down the standard formula of the circumference. Then we separated the diameter from the formula and took everything else to the other side. And we had the relationship. It is necessary to convert the radius in the formula to diameter.