Not understanding what the question is asking. Volume of solid

[Jbreezy]

Homework Statement

Referring to the parallelepiped in Question 3 in which vertices E,F,G,H are respectively the diametrically opposite corners to A,B,C,D . Find the volume, in cubic units of the solid with seven plane faces BGD,BCD,GFD,BHG,GHEF,EFGC,BHEC

Homework Equations

The Attempt at a Solution

I'm not really understanding what it is asking me. I understand finding volumes. Is this telling me to find the volume with each plane face? For instance, BGD. I could make an origin out of F which is diagonal to B and maybe do the volume of a tetrahedron.
I guess I don't understand what it is asking me.

 

[mfb]

I think there is some sketch missing.

Find the volume, in cubic units of the solid with seven plane faces BGD,BCD,GFD,BHG,GHEF,EFGC,BHEC

Is that the exact problem statement? It looks weird. If not, please write it down exactly as it was given.

 

[Jbreezy]

Yeah that was exact I copied and pasted. I will try and draw it when I get back home in a bit. I did draw it but on word I mean. Yeah it is confusing me.

 

[Jbreezy]

OK this is what I have drawn and how I labeled it please ignore the lack of artistic flair. It serves it's purpose though. So I was using this and thinking what the heck is this question asking me?

 

[Jbreezy]

mfb, does it make anymore sense?

 

[mfb]

I don't know how to interpret the question.
You can find the volume as function of the vectors of 3 edges.

 

[Jbreezy]

Yeah, I don't either. That is the exact question though I literally copied and pasted.

 

[haruspex]

I think there's a typo. The last but one face should be EFDC, not EFGC. It's the whole figure less the pyramid ABDG. (Which is a big hint towards the answer.)

 

[Jbreezy]

So, Am I supposed to find the volume with of each thing? Like BHE and EFDC separate? What is meant by the volume of the solid?? thx

 

[Jbreezy]

wait wait wait

 

[Jbreezy]

OK, so I think I got it maybe not.
I found the volume of the parallelepiped to be 16 cubic units from a previous question. So the shape that is formed from ABDG is a tetrahedron which is 1/6 that of a parallelpiped. So 16- (1/6)16 = 40/3 cubic units.

I hope this is correct
Thanks

 

[haruspex]

OK, so I think I got it maybe not.
I found the volume of the parallelepiped to be 16 cubic units from a previous question. So the shape that is formed from ABDG is a tetrahedron which is 1/6 that of a parallelpiped. So 16- (1/6)16 = 40/3 cubic units.

I hope this is correct
Thanks

Looks right.