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For the following question

A cubical block of metal weighs 6 pounds.How much will another cube of the same metal weigh if its sides are twice as long ? Ans=48

Here is how I am solving it but I am getting 12 as the answer

For the current cubical block $12$ edges of cube weigh = 6 pounds

$1$ edge weighs = $\frac{6}{12} = \frac{1}{2} pound$

Doubled edge would weigh $2 \times \frac {1}{2} = 1$ so 12 edges would weigh $12 \times 1 = 12$

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    @martycohen I think the OP assumed it was a metal frame. Hence the concern of using the edges to measure. Double the frame double the weight.2015-10-31

3 Answers 3

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HINT:

  1. Write down the volume of a cube with edge length $x$. Think of an aquarium with all sides equal.
  2. As 1. with length $2x$.
  3. What's the ratio of the volumes?
  4. How heavy is the larger cube?
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    Yeah That makes sense.. Thanks2012-07-24
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We look only at our particular case "twice as long." Note that if you want to construct a $2\times 2\times 2$ cube out of $1\times 1\times 1$ cubes, you will need $8$ of the little cubes. For we need $4$ little cubes at the "bottom," with another $4$ stacked on top of that.

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8 edges of a cube. You have to do 6x8 in order to find your answer because you're doubling the lengths of each side. The logical answer may seem like 12, but the answer is actually 48

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    Cubes actually have 12 edges. The reasoning in your second sentence makes absolutely no sense.2015-11-04