Solving for a different variable

[sboerner]

I need to calculate the sizes of some objects based on volume for a project that I am working on. My math skills are rudimentary – my last experience with algebra would have been in high school, many moons ago – but after much fussing around with online solvers and Excel I've come up with this equation, which solves for volume based on height and a few other variables for the shape I need:

V = πh³/3tan²(a) + πRdh²/180tan(a)

Which combines to:

V = πh²(60h+tan(a)Rd)/180tan²(a)

Now, I'd like to revise this so it solves for h (height) instead of V. The online solvers just throw up their hands when they see this. Me too. Can anyone show me how this might be done? I'd be curious to see the steps. Playing with this reminds me why I enjoyed math so much in school.

Thanks.

 

[Deleted member 4993]

Your function is of the form:

y = A * x³ + B * x²

These cannot be (in general) be inverted using algebraic methods.

You'll need to use numerical method (Newton's algorithm) to approximate the roots.

 

[sboerner]

Thank you, Subhotosh, for the quick reply.

I had a hunch that I'd reached a dead end, algebraically speaking.

It's a very simple matter to plug in estimated values in Excel for the height until I reach the volume that I need. So it works fine as is. But I was curious if it might be possible to invert it.

Now I know. Thanks again.

 

[Deleted member 4993]

Thank you, Subhotosh, for the quick reply.

I had a hunch that I'd reached a dead end, algebraically speaking.

It's a very simple matter to plug in estimated values in Excel for the height until I reach the volume that I need. So it works fine as is. But I was curious if it might be possible to invert it.

Now I know. Thanks again.

Excel has a function called "Goal Seek". Read up on it and see if you can use it here. It will automate the iteration process.

 

[sboerner]

Excel has a function called "Goal Seek". Read up on it and see if you can use it here. It will automate the iteration process.

Wasn't aware of that. Works perfectly, thanks for the tip.