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A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
A. 92 B. 90 C. 82 D. 78 E. 75
1 million liter cube-shaped tank \(= \frac{1,000,000}{1,000} = 1,000\) cubic meter tank, which means that we have the cube-shaped tank with a side of \(10m\) (\(10^3=1,000\)).
Surface area of this tank would be \(6 \text{ (number of faces of a cube)} * 10^2 \text{ (area of each face)} = 600\) \(m^2\).
Number of \(4*2=8\) \(m^2\) sheets needed is \(\frac{600}{8}=75\).
Why does the tank need a cover? This confused me while answering the question. It would be good to make it clear that the tank needs a cover. For a cube-shaped tank that needs to contain 1 million liter only 62.5 sheets are necessary: we need 1 bottom and 4 sides with a required total of 500 square meter. 500/8=62.5. Edit: That would be 63 sheets
I attempted the question with a 3D structure in mind.
Firstly we have a side of cube: 10 m
Secondly now how you could arrange 4 X 2 sheets in a 10 m side.
Interestingly if you draw the sheets in 10 X 10 side, you would only be able to put 12 such sheets in it with area of 2 X 2 remaining (I would try to draw it some other time): 12 X 6 = 72 sheets
Now as there are six sheets (in total) for the cube, so a total of 3 more sheets required to join adjacent sides.
Why does the tank need a cover? This confused me while answering the question. It would be good to make it clear that the tank needs a cover. For a cube-shaped tank that needs to contain 1 million liter only 62.5 sheets are necessary: we need 1 bottom and 4 sides with a required total of 500 square meter. 500/8=62.5. Edit: That would be 63 sheets
Is there a typo in the question? Because if not, then wouldn't we also be able to use 90 sheets of metal (60 in 4x2, and 30 in 2x2, with 15 sheets of metal per side 4x2x10 and 2x2x5) ?
Why does the tank need a cover? This confused me while answering the question. It would be good to make it clear that the tank needs a cover. For a cube-shaped tank that needs to contain 1 million liter only 62.5 sheets are necessary: we need 1 bottom and 4 sides with a required total of 500 square meter. 500/8=62.5. Edit: That would be 63 sheets
Can someone explain this concept?
I also did not understand. Why do we need to consider it with the cover?
Why does the tank need a cover? This confused me while answering the question. It would be good to make it clear that the tank needs a cover. For a cube-shaped tank that needs to contain 1 million liter only 62.5 sheets are necessary: we need 1 bottom and 4 sides with a required total of 500 square meter. 500/8=62.5. Edit: That would be 63 sheets
Can someone explain this concept?
I also did not understand. Why do we need to consider it with the cover?
close
66% (01:26) correct 
