# First time thread! V=4/3 . PI . R^3 Rewrite as R=....

#### keesief

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.

#### MarkFL

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.

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1 person

#### keesief

Edit.... I GOT IT! Because dividing 4/3pi by 3/4pi makes them cancel out! MANNNN O MANN!! Thanks BRO! I love you.

#### MarkFL

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.

#### keesief

Ehmmm Latex? I said I love you but I think your moving to fast 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!

#### the john

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

#### the john

. . . $$\displaystyle =\,\boxed{\frac{1}{2}\sqrt{\frac{A}{\pi}}}$$