Transpose formula for the volume of a cylinder

[mark1987]

Hi all,

I am a mature age student and am taking my first course in maths in over 30 years as next year I am to study surveying.

I have started to learn how to transpose formula and I just need some help on transposing V= pi*r²* h to solve for r.

Though I have tried different methods, I really need some help with this. If you don't mind can someone please go step by step through the transposing.

My first problem is I have no idea on where to start and in which order, i.e do I divide h first to remove from one side of the equation or do I divide by pi first or do I square root V to remove the square from the radius first?

Any help and advice would be very much appreciated. Thank you.

Mark

 

[daon2]

Hi all,

I am a mature age student and am taking my first course in maths in over 30 years as next year I am to study surveying.

I have started to learn how to transpose formula and I just need some help on transposing V= pi*r²* h to solve for r.

Though I have tried different methods, I really need some help with this. If you don't mind can someone please go step by step through the transposing.

My first problem is I have no idea on where to start and in which order, i.e do I divide h first to remove from one side of the equation or do I divide by pi first or do I square root V to remove the square from the radius first?

Any help and advice would be very much appreciated. Thank you.

Mark

To solve for r, first you must solve for r^2. You have V=pi*r^2*h. You wish to rid yourself of the pi and h which are "attached" to r^2 by multiplication. To get rid of them you must apply the *inverse* operation: division. Fortunately, because multiplication is commutative, the order in which you this does not matter. You may first divide both sides by pi, or h, or you may combne it all into once step: divide by pi*h.

Once you get r^2 by itself, you apply the *inverse* of the square operation (the square root) to both sides to get r by itself. In general, the square root operation does not produce a unique value: \(\displaystyle x^2 = a\) does not imply \(\displaystyle x=\sqrt{a}\), but rather one of two possibilities: \(\displaystyle x = \sqrt{a}\) or \(\displaystyle x=-\sqrt{a}\). However, in this case, it is clear that r is a radius, and is a positive quantity, so you may assume \(\displaystyle \sqrt{r^2}=r\).

 

[mark1987]

Thanks

Hi,

Thank you to Soroban and Daon2,

Your explanations have assisted me greatly. Thanks once again.

Mark

 

[mmm4444bot]

Soroban! Stop using that white marker!