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
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.
Hi Tay, thank you.
Hi ATM, don’t mention.
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 |
hi dazzlego, thank you.
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 | 8510cm^{3} | 8510/90=94.5cm^{3 }(approx vol. per cube) |
4^{3}=64, 5^{3}=125, so select 4cm-cubes |
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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 |
**37/9 =4 1/9 cm |
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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!
HI SAHMOM, thank you so much.