so if area of circle = pie * r^2 , then how do you get area of circle = (pie/4) * diameter^2


I know you can just do diameter * 0.5 = radius. and then do the normal pie * r^2

but i want to know how do you get from pie * r^2 = (pie/4) * diameter^2 ?

A = pi * r^2
= pi/4 * 4r^2
= pi/4 * (2r)^2
= pi/4 * diameter^2. , where 2r=diameter


I graduated from elementary school today 👌

This post was edited by Zekdawg on Jul 1 2017 09:15pm

He skipped a step or two, but he did it correctly.


Just make a fictitious circle with r=3 and d=6, and do the substitution to check his result for yourself

ok thanks, but on the first step,how can you multiply the radius^2 by 4 and divide pi by 4? you cant just throw in a division and multiplication for the same side of an equation?

He skipped a few steps.

Gimme a sec...


/e Took a while. I'm old, I do math on paper.

A=pi*r^2 ...and r=1/2*d or d/2

So...

A = pi * (d/2)^2

A = pi * d^2/4

A = pi/4 * d^2


This post was edited by Ghot on Jul 1 2017 09:50pm

dividing by 4 amd multiplying by 4 is like multiplying by 1 ; it is just a common trick used in proofs and does not change any factual values

just figured it out

so if radius = diameter /2 , same as r = d/2
then 2 r = d
then d^2 = 4 (r^2)

so d^2 = 4 (r^2)
then r^2 = (d^2) / 4

then you have area = pie * r ^2
substitute r ^ 2 for the above (d^2) / 4
that gives you ( pie * d^2 ) / 4

thanks

This post was edited by noob_whacker on Jul 1 2017 09:49pm

integrate 2pi(r) from r to 0