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A rectangular tank was 23 cm long, 37 cm wide and had a height of 10 cm. Jake managed to fit a maximum of 90 identical cubes into the tank and cover it with a lid. What is the length of one side of each cube?


pls help. thks


23 x 37 x 10 = 8510
Assuming the length of one side of each cube is a whole number, 4 cm.
23 ——- 4 x 5 R3
37 ——- 4 x 9 R1
10 ——- 4 x 2 R2
5 x 9 x 2 = 90

Ans : 4 cm.

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Hi Tay, thank you.

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Hi ATM, don’t mention.

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Not sure if there are other method to solve this,

But you can use “guess and check” to find the solution.


small cube size length 23 cm width 37 cm height 10 cm total cubes
2 cm 11 cubes 18 cubes 5 cubes 11 x 18 x 5 = 990
3 cm 7 12 3 7 x 12 x 3 = 252
4 cm 5 9 2 5 x 9 x 2 = 90
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hi dazzlego, thank you.

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Question should specify clearly that the sides of the cubes is a whole number. Otherwise, below some non-whole number answers are theorectically acceptable.

  Length Breadth Height Volume +Working
Tank 23cm 37cm 10cm 8510cm3 8510/90=94.5cm(approx vol. per cube)

43=64,   53=125,   so select 4cm-cubes

Check: No. of 4cm-cubes 5 pcs 9 pcs 2 pcs 5x9x2=90pcs OK. Only answer if side of cube is in whole number. If so, end of solution#
For some fun  


=4 1/9 cm

No. of 4 1/9 cm-cubes 5 pcs 9 pcs 2 pcs 5x9x2=90pcs Acceptable answer*
No. of 3.9 cm-cubes 5 pcs 9 pcs 2 pcs 5x9x2=90pcs Acceptable answer*

* Is the setter looking for non-whole number answers? I doubt so since there is a range of answers acceptable and the question asks what is “the” length. It is likely a careless omission by the setter. Then any student who can show reasonable working for getting acceptable answer should also be marked correct. It would be a fun discussion question to share with students so they know the intricate details to take note of in Maths and the difference it makes. To challenge and question a question. I used to make use of such opportunities to “scare” DC why there are A* and A students for DC to “wake up” and work harder for exams. 🙂

Further question for those who really like challenges is to purposely not mention “whole number sides” and ask what is the “maximum” side of the cube and answer is 4 1/9 cm for this question.

**This side is the most constrained side. So maximum length is restricted by this side.

All the above observation is because I gave myself a little push to find what is the maximum (non-whole number) length of cube since the question did not mention that the sides of cube must be whole-number. Then I found 4 1/9 cm. Then I ask myself if 3.9 cm can work and it works also.

Last but not least, have fun!

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HI SAHMOM, thank you so much. 

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