My Math Forum First time thread! V=4/3 . PI . R^3 Rewrite as R=....

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 April 7th, 2014, 09:17 AM #1 Newbie   Joined: Apr 2014 From: Holland Posts: 3 Thanks: 0 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.
 April 7th, 2014, 09:44 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 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...
 April 7th, 2014, 10:18 AM #3 Newbie   Joined: Apr 2014 From: Holland Posts: 3 Thanks: 0 Edit.... I GOT IT! Because dividing 4/3pi by 3/4pi makes them cancel out! MANNNN O MANN!! Thanks BRO! I love you.
April 7th, 2014, 10:23 AM   #4
Senior Member

Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Quote:
 Originally Posted by keesief 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.

 April 7th, 2014, 10:25 AM #5 Newbie   Joined: Apr 2014 From: Holland Posts: 3 Thanks: 0 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!
 April 8th, 2014, 01:57 AM #6 Senior Member   Joined: Mar 2014 Posts: 112 Thanks: 8 $\displaystyle \boxed{r\,=\,\sqrt[3]{\frac{3V}{4\pi}}\,=\,\sqrt{\frac{A}{4\pi}}}$
 April 8th, 2014, 02:00 AM #7 Senior Member   Joined: Mar 2014 Posts: 112 Thanks: 8 . . . $\displaystyle =\,\boxed{\frac{1}{2}\sqrt{\frac{A}{\pi}}}$

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# 4/3pir^3

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