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Volume of Rectangular Prisms

Directions: Using the digits 1 through 9, at most one time each, fill in the boxes to create 2 rectangular prisms so the volume of one rectangular prism is double the volume of the other rectangular prism.



How can we find the volume of a rectangular prism?
What does it mean for one quantity to be double another’s?



There are many possible answers.
One possible answer is a rectangular prism with dimensions of 2 by 8 by 9 would have a volume of 144 cubic units which is double the volume of one with dimensions of 4 by 3 by 6 (72 cubic units).

Another possible way is an 8 by 6 by 1 (48 cubic units) is double one with dimensions of 2 by 3 by 4 (24 cubic units).

Source: Joe Schwartz

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  1. Joe Schwartz,
    This is a great problem!

    However, I found the directions to be some what misleading. They say to use the digits 1 – 9, EACH only once. I expected to be using nine digits for the six dimensions, which means three of the dimensions would need to be double digit numbers. When I checked the answer, I saw that you did not intend for EACH DIGIT to be used.
    Perhaps you intended that I was to select only single digit numbers from the digits 1-9, and that no digit could be used more than once?

    Do you think there is a solution for the problem as originally written, using each of the digits 1-9 only once?

  2. Should the directions read “the volume of one rectangular prism is double the volume of the other rectangular prism”? You can’t find the volume of a rectangle…at least you couldn’t the last time I checked 🙂

    • I love this problem. When I first attempted this problem I was thinking in terms of volume formula and I fell flat on my face. I realized in my second attempt that I had to actually visualize the layers within the prisms and then it was easy. What a great task for conceptual knowledge! Also, I agree with Sarah, the wording should be rectangular prism not rectangle.

  3. What about units?

  4. Never telling my name

    6 height, 4 width, and 2 length is 48 cubic units and 3 height, 1 width, and 8 length is 24 cubic units.

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