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# A cubical block of metal weighs 6 pounds. How much will another cube

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Math Expert
Joined: 02 Sep 2009
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A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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03 Apr 2015, 04:10
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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?

A. 48
B. 32
C. 24
D. 18
E. 12

Kudos for a correct solution.

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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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03 Apr 2015, 07:01
5
A

suppose side of given cube is x
now weight relates to volume

x ^3=6pounds

side increased twice to 2x

8x^3

so weight increases by 8*6=48
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A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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03 Apr 2015, 04:25
Bunuel wrote:
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?

A. 48
B. 32
C. 24
D. 18
E. 12

Kudos for a correct solution.

Pick numbers approach:
For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 6 pounds

If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 6 pounds = 48 pounds

And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3

we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
6 * 8 = 48
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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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03 Apr 2015, 08:32
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Bunuel wrote:
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?

A. 48
B. 32
C. 24
D. 18
E. 12

Kudos for a correct solution.

$$a^3$$=6

a--->2a

$$(2a)^3$$=$$8a^3$$
=8*6
=48

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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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05 Apr 2015, 00:12
1
Suppose length of side of a cube =x; there fore x^3 =6
if length is increased by 2X, volume would be 8x^3=8*6=48

Thanks,
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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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05 Apr 2015, 00:49
1
Bunuel wrote:
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?

A. 48
B. 32
C. 24
D. 18
E. 12

Kudos for a correct solution.

Volume of first cube= 6
Therefore side=cube root 6
And, side of second cube= 2*cube root 6
Volume of second cube=8*6=48. Answer =A
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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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05 Apr 2015, 20:23
1
question is framed in terms of weight to add some confusion. basically it boils down to volume of a cube!
give cube has a vol = 6.
If sides were twice the original : s - 2s
Volume would be : (2s)^3 => (givenVol)*2^3
Thus : 6*8 = 48.
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Posts: 64174
Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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06 Apr 2015, 05:43
Bunuel wrote:
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?

A. 48
B. 32
C. 24
D. 18
E. 12

Kudos for a correct solution.

OFFICIAL SOLUTION:

If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.

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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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15 Mar 2016, 18:18
I'm really confused on how to do this problem? Many confusions in the replies. Could someone please clarify in a more simpler terms?
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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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15 Mar 2016, 18:31
leonidbasin1 wrote:
I'm really confused on how to do this problem? Many confusions in the replies. Could someone please clarify in a more simpler terms?

hi,

The Q is
Quote:
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?

A. 48
B. 32
C. 24
D. 18
E. 12

what is cuboidal?

Like a brick with all equal sides..

How is weight related to it?

If you increase the size of each side, the weight will increase..

If you have a bucket of water, you fill up more water, the weight will increase..

what is happening in each case of BRICKS and WATER..
we are increasing the quanity and weight increases..
this increase in quantity is same as increase in VOLUME..

SAME is the case here..

A cube has VOLUME as a^3 when the side is a..

Now side is made 2a, so volume= (2a)^3=8a^3
now if a^3 weighs 6, 8a^3 will weigh 8*6=48

Hope it helps

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Re: A cubical block of metal weighs 6 pounds. How much will another cube  [#permalink]

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10 Dec 2019, 17:31
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Re: A cubical block of metal weighs 6 pounds. How much will another cube   [#permalink] 10 Dec 2019, 17:31