A welder needs to construct a closed cube-shaped tank with a volume of

Question

A welder needs to construct a closed cube-shaped tank with a volume of 1 million liters. If the welder has access to only 4x2 meter sheets of metal that can be cut, and 1 cubic meter is equivalent to 1,000 liters, how many sheets of metal will be required to construct the tank?

A. 92
B. 90
C. 82
D. 78
E. 75

Bunuel · Accepted Answer

Official Solution:

A welder needs to construct a closed cube-shaped tank with a volume of 1 million liters. If the welder has access to only 4x2 meter sheets of metal that can be cut, and 1 cubic meter is equivalent to 1,000 liters, how many sheets of metal will be required to construct the tank?

A. 92
B. 90
C. 82
D. 78
E. 75

Since 1 cubic meter = 1,000 liters, then 1 million liter tank  = \frac{1,000,000}{1,000} = 1,000  cubic meter tank.

1,000  cubic meter tank, means that each side of the cube-shaped tank is 10 meters long (since 10^3 = 1,000).

The surface area of this tank would be  	ext{ (number of faces of a cube)} *	ext{ (area of each face)} =6*10^2= 600  square meters.

Since each sheet is  4*2=8  square meters, then to cover 600 square meters of area,  \frac{600}{8}=75  sheets will be needed.

Answer: E

mikemcgarry · Answer

Hi, there! I'm happy to contribute here!

The question say: A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)

In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.

A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).

The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.

The question tells us: he has only 4x2 meter sheets of metal that can be cut.

Each sheet has an area of 8 sq m. How many of these need to fill up 600 sq m? 600/8 = 75. He needs 75 sheets.

Answer = E

It appears that both Mr. Bunuel and I got the same answer, different from the OA you posted. Perhaps you miscopied.

Please let me know if you have any questions on this.

Mike

jlgdr · Answer

10^5 for volume in a cube implies 10^2*10^2*10^2 which means that the surface area of a side is 10^2. Well, we want to build the total surface area so if cube has 6 sides then 6*100 = 600. Since the area covered by each sheet is 8 , then we have 600/8 = 75 sheets needed

E

Let me know if this is clear
Cheers
J

E

Let me know if this is clear
Cheers
J

mikemcgarry · Answer

Dear jlgdr , Forgive me, my friend, but I am going to correct a couple of mistakes in your approach, in an attempt to strengthen your understanding as well as the understanding of anyone else who chances upon this post. First of all, 1 million = 1,000,000 = 10^6, not 10^5. Second, the 1 million in this problem is 1 million liters , and the liter is a unit of volume. If you say that the cube is 10^2 = 100 on each edge, then that's 100 whats? a 100 cube-roots-of-a-liter?? You see, something becomes really funky about the units here. (In fact, a liter is a cubic decimeter, that is, a cube that is 10 cm on each side, but that would put the side of the cube at 100 decimeters, a most peculiar unit to employ.) Finally, if the cube really were (10^2)*(10^2)*(10^2), then (10^2) would be the length of an edge, and (10^2)*(10^2) = 10^4 would be the area of a face. In general, if a cube has volume L^3, it has edge-length L, and each face has an area of L^2. Your mistakes canceled, so you wound up with the correct answer. It's very important to appreciate when you get a question correct for correct reasons, and when you get it correct for incorrect reasons. I hope all this helps. Mike :-)

Saurabhminocha · Answer

Volume of tank = 10^6 liters -> 10^6/10^3 cubic m = 10^3

Volume of cube = a^3 -> a = 10 m
Surface area of cube = 6a^2 = 600 squared m
Area of one sheet = 4*2 = 8 squared m

N = 600/8 = 75 (E)

ScottTargetTestPrep · Answer

Solution:
 
Since 1,000 liters = 1 cubic meter, then 1,000,000 liters = 1,000 cubic meters. Therefore, a 1 million liter cube is a 1,000 cubic meter cube. Such a cube will have an edge length of 10 meters and a surface area of 6 x 10^2 = 600 square meters. Since each sheet of metal is 4 x 2 = 8 square meters, we need 600/8 = 75 such sheets to construct (the surface) of the cube-shaped tank.

Answer: E

smmc29 · Answer

Convert cubic liters to cubic meters:

1 million liters = 1000 cu.m.

Side of cube = cuberoot of (1000) = 10m.

Get the surface area of the cube = 6s^2 = 6(10)(10) = 600

Get number of metal sheets:

SA cube / A metal sheets

= 600 / 8 = 75.

E is the correct answer.

saynchalk · Answer

Can this question come for GMAT focus edition?

Bunuel · Answer

Yes, I believe so. This is a word problem involving some rudimentary geometry knowledge, which is considered by the GMAT as general knowledge rather than specific geometry.

saynchalk · Answer

Alright sounds good, thanks Bunuel!

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A welder needs to construct a closed cube-shaped tank with a volume of

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