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April 7th, 2014, 09:17 AM   #1
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First time thread! V=4/3 . PI . R^3 Rewrite as R=....

Hello Peeps, this is my first time posting. My name is Kees I'm 23 years old and Im from Holland.

I am a carpenter atm but will start my education to be a construction supervisor which will take 4 years.

Recently I started taking math classes and just got my fist grade 7.4! (out of 10) So I was happy since I never had math before.

Anyways, Now I am at chapter 9 of my book and I frequently get asked to do formulas like;

V=4/3 . PI . R^3

Rewrite as R

Now since I am taking a speed course, my teacher doesn't really have the time to go step by step to solve the problem.

I was hoping somebody could help me with this.

Kind regards, Kees.
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April 7th, 2014, 09:44 AM   #2
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Hello and welcome to MMF, Kees!

We are given the formula for the volume$V$ of a sphere in terms of its radius $r$:

$\displaystyle V=\frac{4}{3}\pi r^3$

And we are asked to solve for $r$. The first thing we want to do is multiply both sides by $\displaystyle \frac{3}{4\pi}$ so that we just have $r^3$ on the right sides:

$\displaystyle \frac{3}{4\pi}\cdot V=\frac{3}{4\pi}\cdot\frac{4}{3}\pi r^3$

Divide out the common factors on the right and arrange as:

$\displaystyle r^3=\frac{3V}{4\pi}$

Next, we want to take the cube root of both sides so that we just have $r$ on the left:

$\displaystyle \sqrt[3]{r^3}=\sqrt[3]{\frac{3V}{4\pi}}$

$\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}$

This will allow us to determine the radius of a sphere if given the volume.
Thanks from keesief

Last edited by MarkFL; April 7th, 2014 at 10:26 AM. Reason: minor typo...
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April 7th, 2014, 10:18 AM   #3
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Edit.... I GOT IT! Because dividing 4/3pi by 3/4pi makes them cancel out! MANNNN O MANN!! Thanks BRO! I love you.
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April 7th, 2014, 10:23 AM   #4
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Quote:
Originally Posted by keesief View Post
Man I actually think I get it. You divide by $\displaystyle 3/4PI$ because $\displaystyle 4/3 times pi$ is $\displaystyle 4pi/3$ right? I mean that 3/4pi is the opposite right?
Yes, $r^3$ originally has the coefficient of $\displaystyle \frac{4\pi}{3}$, so if we multiply both sides by the reciprocal or multiplicative inverse of this coefficient, then we will be left with a coefficient of 1.

Incidentally, to write fractions with $\LaTeX$, use the command:

\frac{numerator}{denominator}

and to write special characters like $\pi$, use the command \pi.
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April 7th, 2014, 10:25 AM   #5
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Ehmmm Latex? I said I love you but I think your moving to fast :P Jk. Thanks for your help mark. I am gonna continue with my homework. You help me get one step closer to my goal of being a supervisor in construction!

I'll be back!
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April 8th, 2014, 01:57 AM   #6
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$\displaystyle \boxed{r\,=\,\sqrt[3]{\frac{3V}{4\pi}}\,=\,\sqrt{\frac{A}{4\pi}}}$
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April 8th, 2014, 02:00 AM   #7
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. . . $\displaystyle =\,\boxed{\frac{1}{2}\sqrt{\frac{A}{\pi}}}$
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