# Changing the subject of an equation

• May 24th 2012, 07:20 AM
LordMigit
Changing the subject of an equation
Hi guys! I am just looking for a little theory help to do with changing subjects of an equation.

For instance
Code:

v = 4/3πr3
a simple formula for working out the volume of a sphere. But I want to change the subject to r. So my question is, when you do something to both sides of an equasion, does it apply to each element of that side of the equation.

For example changing the subject to r, my first inclination would be to multiply both sides by 3 so as to get rid of the fraction preceding Pi. (this may be wrong but its just an example.) So would i end up with
Code:

3v = 4πr3
or
Code:

3v = 4π3r3
???

Appologies for the X formating, i have not got used to the text editor on the forum yet.

... watch your language.
• May 24th 2012, 08:40 AM
skeeter
Re: Changing the subject of an equation
$\displaystyle V = \frac{4\pi r^3}{3}$

$\displaystyle 3V = 4\pi r^3$

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

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