IMPORTANT, Volume of decahedron (1 Viewer)

[VQ]

Does anyone know how to calculate the volume of decahedron (well, they said it is called as decahedron, a solid consist of 10 sides)? What is the shape of the sides of the decahedron anyway?

 

[KFunk]

http://mathworld.wolfram.com/Decahedron.html ... take your pick.

 

[Slidey]

Dodecahedra are so much better than decahedra.

http://mathworld.wolfram.com/Dodecahedron.html

If you mean a regular decahedron, then... I have no idea. With lots of triangles and free time, I'd imagine.

 

[withoutaface]

Now the real question is can I be bothered making a wireframe of such a shape for my CAD assignment.
*ponders

 

[want2beSMART]

the area is pretty simple...

but you have to give us some more information...and seems damn hard

are you asking us for the fun of it?

 

[dawso]

its ANY shape with 10 sidea, includin a octagonal prism, lol, just do this, make an octagon, fnd area, times by height?? is the question any more??

 

[dawso]

yes, thats y i said dependin on what the question asked, but steele, thats still simple, i cant rememeber wat the sides are, but say its 10 triangles, just 10 times the volume of that pyramid, im assumin this is a variable volume but, but u would just do 10 times the integral appropriate to that pyramid...

 

[Slidey]

Who said a regular decahedron looks like a pyramid, though?

Take a look at the wolfram site on dodecahedra.

 

[dawso]

what i actually meant by the regular decahedron was similar to the regular dodecahedron, to do this, it is simply 12 pyramids, but from the site on the decahedron there isnt a 'regular' dodecahedron so with the question posed as it is, 'find the volume of a decahedron' there are an infinite number of solutions...

 

[want2beSMART]

can this question even be solved?

 

[VQ]

No...it's just some sort of extra marks or whatever...but really, I am curious about it...

I found out that the base of decahedron (10 sided) is a kite, we can cut it somehow...But I can not imagine the shape of the cut-off, should it be some sort of a pyramid? and how to calculate the height? By angle? And what is the angle anyway? Confusing....

Dodecahedron (12 sided)'s base is a pentagon. We can cut dodecahedron into 12 similar pyramid with the base of pentagon. The height can be known by angle...I found it when I browsed through, but forget the name of the website >.<

My friend said that isodecahedron? ehh...something with 20 sided's base is equilateral triangle so you can cut it into 20 pyramid and found the volume, again the height????

Umm, anyway...so what's the use of integral in this case beside finding the formula of pyramid being 1/3*base*height (am I true, anyway?)....is there any method, cylindrical or slicing that can be used to solve the problem of the volume of any shape with more than 10 sided (start from decahedron)? Anyone can help?

 

[want2beSMART]

extra marks? so how do you get the marks?

this would be impossible to find out...unless we experiment with it