Solve Ali's Solid Volume Puzzle: 9 Faces, 27 cm^3 Cubes

[thereddevils]

Homework Statement

Ali is making solids out of cubes . Each cube has a volume of 27 cm^3. The diagram shows one solid Ali made . It has 10 faces and a volume of 108 cm^3. Ali made a solid out of the cubes that has 9 faces.What is the smallest volume in cm^3 the solid could have?

Homework Equations

The Attempt at a Solution

 

[Axiom17]

Have you done any calculations yet? What's your attempt at this so far?

 

[thereddevils]

Have you done any calculations yet? What's your attempt at this so far?

I tried rearranging those cubes to get a solid with 9 faces. Any hints?

 

[Axiom17]

Good start I've tried that approach too, but.. is it even possible?!

I can only seem to be able to get either 6, 8, or 10 sides, when arranging those 4 cubes, and I'm sure I've tried all possible combinations as I suppose you have done already as well.

The question seemed to imply that only those 4 cubes were used, but not sure if maybe then you can use as many as you like. Would certainly seem to be more possible then.

 

[njama]

I think the question asks for as many cubes as you like.

Start with
1 cube: 5 faces;
2 cubes: 5 faces, 10 faces;
3 cubes: 5 faces, 8 faces, 10 faces, 15 faces;
4 cubes: 5 faces, 8 faces, 10 faces, 13 faces, 15 faces, 20 faces;

Now you try, and give me the answer.

 

[Axiom17]

.. I see a pattern!