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In 8 unit cubes, how many different rectangular prisms can i build?

2 Answers

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Final answer:

Using 8 unit cubes, one can build three different rectangular prisms, considering the possible integer dimension combinations that make up the number 8.

Step-by-step explanation:

To determine how many different rectangular prisms one can build using 8 unit cubes, we need to consider the possible ways to arrange these cubes so that they form a prism. A unit cube has dimensions of 1x1x1, so we are looking for all the integer factor combinations of 8 that will result in a rectangular prism. The factors of 8 are 1, 2, 4, and 8. These factors give us the following distinct rectangular prisms:

  • 1x1x8
  • 1x2x4
  • 2x2x2

It's important to note that the prism 2x4x1 and 4x2x1 are not included separately as they are the same as 1x2x4 when rotated. Therefore, we have a total of three different rectangular prisms that can be formed with 8 unit cubes.

User Shemona Puri
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5 votes


((n-1)(n)(n+1))+n=n^3


User Arlind Hajredinaj
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