Question

Question #e3bdf

Answer 1

See a solution process below:

Explanation:

To solve this problem we must solve the Area formula for `r`. First, we need to divide each side of the Area formula by `color(red)(pi)` to isolate the `r` term while keeping the equation balanced:

`A/color(red)(pi) = (pir^2)/color(red)(pi)`

`A/pi = (color(red)(cancel(color(black)(pi)))r^2)/cancel(color(red)(pi))`

`A/pi = r^2`

Now, we can take the square root of each side of the equation to solve for `r` while keeping the equation balanced:

`sqrt(A/pi) = sqrt(r^2)`

`sqrt(A/pi) = r`

`r = sqrt(A)/sqrt(pi)`

We can now substitute this solution for `r` in the formula for diameter:

`d = 2r` becomes:

`d = 2 xx sqrt(A)/sqrt(pi)`

`d = (2sqrt(A))/sqrt(pi)`

Answer 2

`d=2sqrt(Api)` see below for why.

Explanation:

We have two equations here, one for diameter and one for area. To solve this we want to get a formula for diameter that has area in it, or uses `A` in the equation.

`d=2pir`
`A=pir^2`

So to do this what we need is to solve the `A` equation for `r` so we can plug that into the `r` in the `d` equation.

To do this we divide each side by `pi` and square root both sides.

`A/pi = (pir^2)/pi`
`A/pi = r^2`
`sqrt(A/pi)=sqrt(r^2)`
`sqrt(A/pi)=r`

Now we plug what we have for `r` in terms of `A` into our equation for `d`.

So:

`d = 2pir`
`d=2pi(sqrt(A/pi))` From here we are done, just need to simplify
`d=2(sqrt(pi))^2(sqrt(A/pi))`
`d=2sqrt(Api)`

I hope that helps!