Question

Make a formula to find the of the diameter 'a' if the area is 'A'. ​

Answer 1

`2\sqrt{(A)/(\pi)} = a`

Explanation:

I am assuming that you are referring to the diameter and area of a circle. If this is false, then please note that my answer is wrong.

Ok, we know that the area formula for a circle is A =
`\pi r^(2)`, where r is the radius.

We also know that the diameter, a, is two times the radius. Thus,
`a = 2r`, which also means that
`(1)/(2) a = r`. This means that we can substitute the radius (r) with half the diameter (
`(1)/(2)a`) in the area formula equation:

`A = \pi *((1)/(2) a)^(2)`

Your question asks us to find the diameter, which means we must solve for, or isolate, the diameter (a):

`A = \pi *((1)/(2) a)^(2)\\(A)/(\pi) =((1)/(2) a)^(2)\\(A)/(\pi) =(1)/(4) a^(2)\\(4A)/(\pi) = a^(2)\\\sqrt{(4A)/(\pi)} = a\\2\sqrt{(A)/(\pi)} = a`