Optimising - minimise surface are for a given volume

[PC_9764214]

New to Mathcad, I'm trying to understand and provide a long hand example of how mathcad can optimise equations with proof so that I can show the calculations and then move onto solve block at some point.  However, the last steps to rearrange the equation by setting it to "0" and solving has stumped me, in order to obtain the critical points!.  The attached file shows where I've got to.  Can anyone advise how I might expand this and achieve my aim ? Thanks.

[Werner_E · Accepted solution]

Looking for something like this:

If you want Prime to do the minimization you would use the "minimize" function, but you can only do this numerically - meaning that you have to provide a value for V and you don't get the exact result (with pi and roots, ...).

Prime 6 worksheet attached

[PC_9764214]

Thank you for taking time to explain the limitations of the software and how to achieve the calculation in view of those limitations.  Your explanation has helped me understand these limitations and will look to build on your advice to get more confidence in the way I use Mathcad to develop solutions.  If there are any manuals, books or websites you would recommend to help expand my knowledge (A level, k12) I would appreciate that too, if your able to provide that.  Thanks again for your advice.

[Werner_E]

Even though it sometimes may be cumbersome and annoying, I won't necessarily see it as a limitation that Prime forces you to use functions when you define a quantity that depends on other quantities.

According to literature I can't suggest any literature. One of the few books on Mathcad Prime (I don't think its the only one, or is it?)  people usually mention here when asked for literature is the book by Brent Maxfield "Essential PTC Mathcad Prime 3.0". I'm not sure if it really can be recommended - I don't own it and I only leafed through it once - too short for a judgment. If you can find the book in a library, make your own judgment.

There was a lot more literature and a lot of internet sites about real Mathcad (version 15 and older). Much of it is certainly still applicable to Prime, even if the interface looks different. I have fond memories of Philip Pritchard's book "Mathcad: A Tool for Engineering Problem Solving", but you would have to decide for yourself whether this is useful for you.

I learned Mathcad mainly through trial and error with the program, and the predecessor of this forum was a great help to me in this, too.

PTC posted a series of introduction tutorials for Prime here in the forum (more or less useful) but this forum has no documents section, so those posts  are now lost in the expanse of the forum and are relatively difficult to find.

I could find this one
https://community.ptc.com/t5/PTC-Mathcad/Problem-Solving-Using-Physics-Examples/m-p/449703

but as far as i remember there were also others.

EDIT: Just found that the above link is just sort of a subdirectory of this one: https://community.ptc.com/t5/PTC-Mathcad/PTC-Mathcad-All-Worksheets/td-p/450684