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!