Question #e3bdf

2 Answers
May 25, 2017

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)

May 25, 2017

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!