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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)
Step 1) We need 1,000,000 liters, so we use the formula above to get 1,000 m^3.
Now we forget about liters completely and focus on 1,000 m^3.
Step 2) To get volume = length x width x depth. The tank is cubed, which means that all sides should be equal. So cubed root of 1,000 m^3 = 10 m. Now we have our length = 10m, width = 10 m, and depth = 10m.
Step 3) To get the area of one side = length x width = 10m x 10m = 100m^2.
Imagine a six sided die, all sides are 100m^2.
Now to find out how many sheets are required, the problem changes to a surface area problem. Since the sheets will go on the outside (surface area) of the cube.
A smith received an order to make a 1 million liter cube-shaped tank (note that 1 cubic meter = 1,000 liters of water). If he has only 4 meter by 2 meter sheets of metal that can be cut, how many metal sheets will be required for this order if the smith has to make the sides first and then weld them?
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 = 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 (# of faces of a cube) * 10^2 (area of each face) = 600 m^2.
How many facets does a cube have? It has 6 facets. In this case each facet will have the area of 10*10 meters. This is why we need 6*10*10=600 square meters of metal. _________________
Oh my god! HOw can i do this g8 blunder? Im losing control on my sense of understanding as test date is coming closer
dzyubam wrote:
How many facets does a cube have? It has 6 facets. In this case each facet will have the area of 10*10 meters. This is why we need 6*10*10=600 square meters of metal.
A smith received an order to make a 1 million liter cube-shaped tank (note that 1 cubic meter = 1,000 liters of water). If he has only 4 meter by 2 meter sheets of metal that can be cut, how many metal sheets will be required for this order if the smith has to make the sides first and then weld them?
I found this one tricky, not because of the maths but because of the physics!!.
I assumed the volume as 1 million litres instead of 1000 cubic metres. However, a quick google search revealed a fundamental problem in my understanding. Volume is "usually" measured in cubic metres and the capacity in litres.. Although IMHO the value in litres also tells us the volume in a way...
Here are the links I read - 1) http://en.wikipedia.org/wiki/Volume- Although it says that "Volume is commonly presented in units such as cubic meters, cubic centimeters, liters, or milliliters.", it clarifies a little below that "Volume and capacity are sometimes distinguished"
I do stuff like that all the time. It usually means I'm getting I:
A. Have been spending too much time studying and have begun to overthink/overanalyze and it actually starts to take away from my ability to solve questions. You get paranoid looking for tricks so much so that obvious things get lost in the shuffle. When this happens its time for a break. Atleast an hour or two, sometimes the rest of the night, sometimes a full day. Just get your mind off of it.
B: If I'm well rested it means I'm not focused enough. There is no subsitute for full concentration. Just break it down into bit sized pieces and let the answer come to you.
I took a different approach (and ended up using more time, so not recommended).
For a cube to fit 1000 cubic meter of water, each side should be 10 m in length. That means a cube with dimensions 10x10x10 is needed.
Or, each face with 10x10 dimensions. So the question is, how many plates would be required for making one face ? If you draw a basic figure, it would come out to be 12.5 . Since we have 6 faces, 12.5 * 6 = 75, Hence answer E.
No. You've rounded up the answer. The key here is that we can cut the sheets however we need. You have to divide the whole area (600) by the sheet area (8) to get the right answer (75).
saqibbaig wrote:
Take only one side 10*10=100. Now metal sheet 4*2=8 it is clear one side take 13 sheets so 13*6=78 answer is D Am i right
I too did the same mistake in the first go. i.e calculated the number of sheets needed for each side (10*10)/(4*2) = 12.5 so took it as 13 sheets per side hence 13*6 = 78 sheets Now if you read the question again, it asks for how many sheets are needed, No restriction on cutting the sheets. Or you can think like this. 12.5 sheets for 1 side.. so 25 sheets for 2 sides hence 75 sheets for 6 sides. Or simply do 600/8. Hope this helps.
Hi, for those who got D an an answer, which I also got, the mistake is that we have to multiply 6 times 12.5 instead of 6 times 13. The reason is that the surface area of each side of the cube is 100 and needs 12 sheets (each of an area of 8) so the remaining 4 m2 (100 - 96) could be filled up with half a sheet's area, so 12.5 x 6 faces = 75
1 million cubic liter water to be stored. So, capacity of cube should be 1000 cum. Side of cube = 10m. Surface area =6*10*10=600sqm. Number of sheets =Surface area of cube/surface area of 1 sheet = 600/8=75. Its E.
something different from Bunuel...we may to have different language for same kind of questions in PS...so friends need to convert language in numeric contents effectively and efficiently...concentration is the key to success....
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
Hi Experts, Could you please explain the above RED colored part. What does it mean - "1 million liter cube-shaped "? _________________