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

In summary, Ali is creating solids out of cubes and has made one with 10 faces and a volume of 108 cm^3. He is now trying to make one with 9 faces and the smallest possible volume in cm^3. After trying various combinations of cubes, it seems that the minimum volume for a solid with 9 faces is 27 cm^3.
  • #1
thereddevils
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0

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

 

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  • #2
Have you done any calculations yet? What's your attempt at this so far? :smile:
 
  • #3
Axiom17 said:
Have you done any calculations yet? What's your attempt at this so far? :smile:

I tried rearranging those cubes to get a solid with 9 faces. Any hints?
 
  • #4
Good start :smile: I've tried that approach too, but.. is it even possible?! :uhh:

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.
 
  • #5
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.
 
Last edited:
  • #6
.. I see a pattern! :wink:
 

1. What is the puzzle?

The puzzle is called "Ali's Solid Volume Puzzle: 9 Faces, 27 cm^3 Cubes". It consists of a 3x3x3 cube made up of 27 smaller cubes, with each face containing 9 small cubes. The challenge is to rearrange the cubes to form a solid cube with the same volume, but with the colors on each face matching.

2. How do you solve the puzzle?

To solve the puzzle, you need to rearrange the cubes in a specific way. Start by breaking down the cube into smaller sections, such as rows or columns. Then, rotate these sections to create a new formation. Continue to do this until all the colors on each face match and the cube forms a solid shape with the same volume.

3. What are the dimensions of the puzzle?

The puzzle has a 3x3x3 cube shape, with each small cube measuring 1 cm on each side. This means that the overall dimensions of the puzzle are 3 cm x 3 cm x 3 cm.

4. Is there a specific strategy for solving the puzzle?

There are different strategies that can be used to solve the puzzle. Some people prefer to start by focusing on one color and rearranging the cubes to match it, while others prefer to break down the cube into smaller sections and rotate them to create a new formation. Ultimately, the key is to keep experimenting and finding the most efficient way to rearrange the cubes.

5. Are there any tips for solving the puzzle?

A helpful tip is to always keep track of the cube's volume while rearranging the cubes. This will ensure that you are on the right track and have not accidentally changed the volume. It is also useful to pay attention to the colors on the smaller cubes and how they are positioned in relation to each other. This can help guide your moves and prevent you from getting stuck.

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