Doubling the Sides of the Cube

Question

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 $12 \times 1 = 12$

It's a solid cube of metal, not a cubical frame made of 12 edges segments. — Chris Eagle, Jul 24 '12 at 12:39
@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. — fleablood, Oct 31 '15 at 05:35

score 4 · Accepted Answer · edited Apr 13 '17 at 12:21

4

HINT:

Write down the volume of a cube with edge length $x$. Think of an aquarium with all sides equal.
As 1. with length $2x$.
What's the ratio of the volumes?
How heavy is the larger cube?

edited Apr 13 '17 at 12:21

Community

1

answered Jul 24 '12 at 12:44

draks ...

18,449

$x^3 = 6$ so $x=(6)^{\frac{1}{3}}$ so $2x = 2 \times (6)^{\frac{1}{3}} $ this is one side for three sides volume is $48$ – MistyD Jul 24 '12 at 12:48
Hmm, feels like there is something missing. From step 1 we have, $V_1=(1\cdot x)^3$ ok, what is $V_2$ from step 2? – draks ... Jul 24 '12 at 12:51
$x^3 = 6$ so $x=(6)^{\frac{1}{3}}$ so $2x = 2 \times (6)^{\frac{1}{3}} $ this means the new volume would be $(2 \times 6^{\frac{1}{3}}) \times (2 \times 6^{\frac{1}{3}}) \times (2 \times 6^{\frac{1}{3}})$ simplifies to $8 \times 6 $ – MistyD Jul 24 '12 at 12:54
1

ok, just be aware that it's not the volume that is $6$, but the weight of the cube. I thought about $V_2=(2\cdot x)^3=8x^3$, so the larger cube weighs 8 times more than the smaller one. – draks ... Jul 24 '12 at 12:59
Yeah That makes sense.. Thanks – MistyD Jul 24 '12 at 13:00

score 1 · Answer 2 · answered Jul 24 '12 at 14:07

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.

score -1 · Answer 3 · answered Oct 31 '15 at 04:23

-1

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

answered Oct 31 '15 at 04:23

Kennan

1

Cubes actually have 12 edges. The reasoning in your second sentence makes absolutely no sense. – epimorphic Nov 04 '15 at 17:20

Doubling the Sides of the Cube

3 Answers3