Is there a website which literally adds up the bits within the Third stage that shows it does all fit
Not necessary given the massively flawed arguments.
Phase 3 of the Saturn 5 rocket is 61.6 feet tall and 21.7 feet in diameter.
Height measured from where to where?
If it was a cylinder (which it's not the top has a lander attached to it and it's much smaller and the diameter slowly decreases at the top)
That is incorporating both the Instrument Unit (IU) and the Spacecraft/LM Adapter (SLA), neither of which are part of the S-IVB.
I used a cylinder calculator and came up with 22,781 cubic feet.
Remember it's already more than ½ full even if you just literally poured the fuel in the rocket.
Yes, that is literally how most rocket stages work. How much space does he imagine the lines and everything else take up when compared to the volume of fuel?
We still need room for Insulation so now your available space is even smaller.
How thick does he expect the insulation to be? There are many unqualified assumptions being made in his comment that he needs to justify if he claims it supports his conclusions.
Next subtract the cubic feet needed for the rocket's engines.
Go on then? That, again, is his burden of proof. As well as showing that the rocket engine is included in the length of the stage he quotes.
Don't forget the Lander itself.
We still need an oxygen supply, batteries, computers, and room for 3 Astronauts.
None of that was included in the S-IVB stage. The lander sits inside the SLA, and the command/service module sits on top of that. That's a fundamental error in his argument.
That and the fact there are many many diagrams available online that show how everything fitted. Not our burden to go and find the actual answers. His argument fails for being incomplete and making several errors about what needs to be included.
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