Finding surface area and volume of a 6-way PVC pipe

[MrMumbleX]

http://flexpvc.com/cart/agora.cgi?product=PVC-6-ways
Problem: Find the surface area (internal and external) and volume of that (the 6 ways PVC pipe in the link) if the radius of the cavity is .5 cm, the inside of the pipe is completely smooth, and the thickness of the pipes is .05 cm.

I AM NOT ASKING FOR THE ANSWER. HELP BY ANSWERING THE BELOW QUESTIONS:
What field of mathematics (I'm assuming study of the solids of Charles Proteus and integral calculus) should I research in order to solve this problem? Is it a difficult, or long problem? How should I approach this problem? I have no idea as of how to approach this problem. HELP PLEASE!

 

[LCKurtz]

Maybe not what you want to hear, but I would say 3 semesters of calculus might get you to where you could set up and solve that problem.

 

[MrMumbleX]

What if this was the solid?
http://flexpvc.com/cart/agora.cgi?product=PVC-4-ways-side-outlet-Wyes
I'm assuming there won't be much of a difference in difficulty.

 

[LCKurtz]

I think that one would be somewhat more difficult but still the same type of problem.

I'm curious why you are asking this. Do you really care what the volume is? Are you going to study calculus for a year and a half to solve the problem if you can? As a practical matter, if you want the actual volume of those objects you could physically measure the amount of water they displace.

[Edit] Here's a link I found with Google: http://en.academic.ru/dic.nsf/enwiki/3925217

 

[MrMumbleX]

The question was supposed to be my 20 page term paper for math research. One last question, would finding the volume and surface area of this be difficult, and what field of mathematics is involved? Calculus still?
http://www.puzzleworld.org/puzzleworld/puz/hexagonal_prism.htm

 

[LCKurtz]

The question was supposed to be my 20 page term paper for math research. One last question, would finding the volume and surface area of this be difficult, and what field of mathematics is involved? Calculus still?
http://www.puzzleworld.org/puzzleworld/puz/hexagonal_prism.htm

Yes. Probably methods from the third semester of calculus.

 

[MrMumbleX]

Could geometry be used to solve for the volume and surface area of that?

 

[LCKurtz]

I don't know. One of the links I saw said Archimedes had worked out the volume of one of the solids. That was before calculus was invented. Also, Archimedes was smarter than the average bear.

 

[CRGreathouse]

Also, Archimedes was smarter than the average bear.

Heck, probably even smarter than your average human!

 

[alphachapmtl]

3 intersecting cylinders
http://local.wasp.uwa.edu.au/~pbourke/geometry/cylinders/
http://mathworld.wolfram.com/SteinmetzSolid.html
http://www.math.harvard.edu/archive/21a_summer_06/handouts/3cylinder.pdf

 

[RocketSci5KN]

I'm assuming you want an exact calculated number, but if you simply want the answer, I'd model this in Solidworks or similar 3D CAD software and it will give the answers to many decimal places...