Open Middle®
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.
Hint
How can we find the volume of a rectangular prism?
What does it mean for one quantity to be double another’s?
What does it mean for one quantity to be double another’s?
Answer
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).
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
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?
Thanks, I updated the instructions to make this clearer.
The 8 on the second answer should be a 4 because 2 twice the size of that is 4.
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.
Yep. You are both right and this has been corrected.
you can
Yes you can
What about units?
6 height, 4 width, and 2 length is 48 cubic units and 3 height, 1 width, and 8 length is 24 cubic units.
Volume of Rectangular Prisms
left: 1 6 8 right: 2 3 4 so 48 and 24
left: 1 8 9 right: 2 3 6 so 72 and 36
left: 2 8 9 right: 3 4 6 so 144 and 72
Yes; 1 6 8 is the same as 1 8 6 etc but only one such triple is shown above in each case.
Hello! Ms. Pocic’s fifth grade class came up with six different solutions. We are wondering if anyone has any more!
6 x 8 x 3 = 144 and 9 x 4 x 2 = 72
2 x 8 x 9 = 144 and 3 x 4 x 6 = 72
6 x 3 x 2 = 36 and 9 x 8 x 1 = 72
4 x 6 x 1 = 24 and 8 x 3 x 2 = 48
6 x 4 x 2 = 48 and 3 x 1 x 8 = 24
1 x 6 x 8 = 48 and 2 x 3 x 4 = 24
That is 12 different solutions you put.
no derek it isnt
No, there are no other solutions (except for swapping factors around).
My answer was 2 by 8 by 9 would have a volume of 144 cubic units.
Thank you for sending an answer sheet! We are doing remote learning, like so many, and now we’re having to teach math in our household. Having the answer sheet for this problem was helpful for the parents!
Thank you for giving me the answers to the problem 😉
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Hi girl I´m Ms. Linda were bestiess
The bigger one can be 1 by 6 by 8 and the smaller one could be 2 by 3 by 4.
This problem was very hard for a sec but at the end it was very fun and helps a lot with math