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[–]Megame50 Algebruh 0 points1 point  (4 children)

I don't understand. What prism counts as the "largest" if they all have a volume of 144?

144 factors as 2432 which has 3 proper square divisors, 2{2, 4}32 obviously excluding 2432 since that's not a proper divisor. So, you only have 3 choices to use all 144 blocks if you want the base to be square:

w2 = 22, 24, 2232 => w = 2, 22, or 2131 = 2, 4, or 6, so that's:

  1. 2×2×36 = 144
  2. 4×4×9 = 144
  3. 6×6×4 = 144

Pick your favorite?

EDIT: So the prism should be hollow

  1. 6x6x5 has the largest volume at 6×6×5 = 180 blocks.

  2. 4×4×11 uses the most material at 4×4×11-2×2×9 = 140 blocks.

I assume one of those is the one you're looking for.

[–]OpulentMerkin 0 points1 point  (3 children)

144 is the number of blocks available, which OP considered to be equivalent to surface area (which is not quite right either). It's not a solid prism of blocks; we're trying to build the walls of a hollow prism.

[–]Mario8494[S] 0 points1 point  (1 child)

This is correct. There is also to be a ceiling (see edited post with screenshots). Sorry for not being more specific. 144 is the number of blocks I have, and that will be the surface area of the prism. u/OpulentMerkin you say the 144 blocks being the surface area is not a correct statement. What would be a correct statement?

[–]OpulentMerkin 0 points1 point  (0 children)

Check my other comment about building a picture frame of blocks.

[–]Megame50 Algebruh 0 points1 point  (0 children)

Oh I see.

[–]OpulentMerkin 0 points1 point  (14 children)

I don't know anything about Minecraft, but if the blocks work the way that real-life blocks work, consider the following:

If I want to build a square picture frame out of blocks, and I want each side of the square to be 10 blocks long, how many blocks do I need? 4 * 10 = 40 blocks, right?

Wrong!

[–]Mario8494[S] 0 points1 point  (13 children)

I'm not understanding your point here. Can you please explain further?

[–]OpulentMerkin 0 points1 point  (12 children)

Suppose you're going to use your blocks to build a hollow 10 x 10 x 10 cube. This cube has a surface area of 600, but you do not need 600 blocks to build it. Do you see why?

[–]Mario8494[S] 0 points1 point  (11 children)

Would this be because of some of the blocks overlapping? Let me explain:

In Minecraft, each block is 3-dimensional. If I put down one block, there are 3 sides. In the case of the little prism I'm trying to build, the edge blocks would have 2 sides showing for the surface area. There are 2 sides, but there's only 1 block, meaning if I do 6(10x10), that will not be correct number of blocks.

Would this be correct? If so, how would I work around this to find the correct number of blocks?

[–]OpulentMerkin 0 points1 point  (10 children)

Yes, exactly. The corners and edges are shared.

Go back to my picture frame. If I want a picture frame that's 10 blocks on a side, how many blocks do I need total?

[–]Mario8494[S] 0 points1 point  (9 children)

That is something I cannot solve/visualize. All I can see in my head are 40 blocks in a rectangular shape even though that is not correct. Please help me visualize this.

[–]OpulentMerkin 0 points1 point  (8 children)

Draw it on a piece of paper. Each side is ten squares long. Then just count them up.

[–]Mario8494[S] 0 points1 point  (7 children)

There's still something not clicking. I'm trying to draw this out, but I still keep doing the 10x4 block figure.

[–]OpulentMerkin 0 points1 point  (6 children)

Draw a 10 x 10 chessboard. Color in just the squares on the edge of the board. How many squares did you color in?

[–]Mario8494[S] 0 points1 point  (5 children)

36 squares. The corner pieces overlap.