a container has volume 1m cubed
the lenght of the container is 200cm.
list all the possible dimensions of the container.
each dimension is whole number of cm.
What shape is the container ?
rectangle
To find all possible dimensions of the container, we need to consider the relation between volume and length.
The volume of a rectangular container is given by the formula:
Volume = Length × Width × Height
Based on the given information, we know that the volume is 1 m³, which is equivalent to 100 cm × 100 cm × 100 cm = 1,000,000 cm³. Additionally, the length of the container is given as 200 cm.
Now, we can find all possible dimensions by finding pairs of factors that multiply to give 1,000,000 cm³ while keeping the length as 200 cm.
1. Length = 200 cm, Width = 5000 cm, Height = 10 cm
2. Length = 200 cm, Width = 2500 cm, Height = 20 cm
3. Length = 200 cm, Width = 1250 cm, Height = 40 cm
4. Length = 200 cm, Width = 1000 cm, Height = 50 cm
5. Length = 200 cm, Width = 500 cm, Height = 200 cm
6. Length = 200 cm, Width = 400 cm, Height = 250 cm
7. Length = 200 cm, Width = 250 cm, Height = 400 cm
8. Length = 200 cm, Width = 200 cm, Height = 500 cm
9. Length = 200 cm, Width = 125 cm, Height = 800 cm
10. Length = 200 cm, Width = 100 cm, Height = 1000 cm
11. Length = 200 cm, Width = 50 cm, Height = 4000 cm
12. Length = 200 cm, Width = 40 cm, Height = 5000 cm
13. Length = 200 cm, Width = 25 cm, Height = 8000 cm
14. Length = 200 cm, Width = 20 cm, Height = 10000 cm
15. Length = 200 cm, Width = 16 cm, Height = 12500 cm
16. Length = 200 cm, Width = 10 cm, Height = 20000 cm
17. Length = 200 cm, Width = 8 cm, Height = 25000 cm
18. Length = 200 cm, Width = 5 cm, Height = 40000 cm
19. Length = 200 cm, Width = 4 cm, Height = 50000 cm
20. Length = 200 cm, Width = 2 cm, Height = 100000 cm
21. Length = 200 cm, Width = 1 cm, Height = 200000 cm
These are all the possible dimensions of the container, where each dimension is a whole number in cm.