Question

How do you find the diameter of a circle with an area?

Answer 1

Hint:In the given question, we have been given to evaluate the value of the diameter of any circle. We have been given that in the given scenario, we have the area of the circle. Using the value of the area, we have to calculate the diameter. To do that, we assume the area of the circle to be any variable. Then we write the standard formula of the area. 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 area \[\left( a \right)\] of a circle whose radius is \[r\]:
\[a = \pi {r^2}\].

Complete step by step answer:
Let the given area be \[a\]. Let the diameter be \[d\].
We know,
\[a = \pi {r^2}\]
Also, we know that,
\[2r = d\]
Hence, \[a = \pi \times {\left( {\dfrac{d}{2}} \right)^2} \Rightarrow \dfrac{{{2^2}a}}{\pi } = {d^2}\]
Thus, \[d = 2\sqrt {\dfrac{a}{\pi }} \]

Additional Information:
We have to change the radius of the circle to the 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 area is given. To do that, we assumed the area to be any variable. Then we wrote down the standard formula of the area. 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.