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# A certain clay cube has volume 64 cubic inches. If a smaller

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Intern
Joined: 07 Feb 2014
Posts: 3
A certain clay cube has volume 64 cubic inches. If a smaller [#permalink]

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07 Feb 2014, 16:47
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Question Stats:

84% (00:48) correct 16% (00:32) wrong based on 173 sessions

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A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cube?

A. 2
B. 4
C. 8
D. $$\sqrt[3]{4}$$
E. $$2 \sqrt[3]{4}$$
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SVP
Joined: 14 Apr 2009
Posts: 2146
Location: New York, NY
Re: How do you solve this [#permalink]

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09 Feb 2014, 21:21
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Luning,
Is this a GMAT question that you are referring to?

At GMAT Pill, we first try to set up the question.

So x*x*x = 64
x^3 = 64
So that means x = 4.

But now you're saying the volume is split in half. So the volume must now be divided by 2...how do we find the length?

So you should take 64 and split it in half to get 32. But the length still needs to be cubed to get to 32.
So use a variable y and say y^3 = 32.

Intern
Joined: 14 May 2014
Posts: 44
Re: A certain clay cube has volume 64 cubic inches. [#permalink]

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19 May 2014, 10:47
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KUDOS
Volume of first cube = 64 cubic inches
Volume of Second cube = Half of First cube's volume = 64/2 = 32 cubic inches
Now volume of a cube = edge^3
hence, edge = volume^(1/3)
In this case, edge = 32^(1/3) = 2* (4)^(1/3) hence E
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Joined: 02 Sep 2009
Posts: 44352
A certain clay cube has volume 64 cubic inches. If a smaller [#permalink]

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19 May 2014, 23:55

Hope this helps.
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Intern
Joined: 14 May 2014
Posts: 44
Re: A certain clay cube has volume 64 cubic inches. If a smaller [#permalink]

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21 May 2014, 10:27
Volume of cube A/Volume of cube B = [Side of cube A/ side of cube B] ^3

here Volume of Cube A = 64
Volume of Cube B = half of 64 = 32
side of cube A = 64^(1/3) = 4
side of cube B = x

putting values

(64/32) = (4/x)^3

2^(1/3) = 4/x
x = 4/2^(1/3) = 2^2/2^(1/3) = 2^(5/3) =2*2^(2/3) =2 * cubic root (4)

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Re: A certain clay cube has volume 64 cubic inches. If a smaller [#permalink]

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30 Sep 2017, 21:48
Luning1 wrote:
A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cube?

A. 2
B. 4
C. 8
D. $$\sqrt[3]{4}$$
E. $$2 \sqrt[3]{4}$$

Volume of cube = 64 in^3
Volume of smaller cube = 32 in^3

So side of smaller cube = $$\sqrt[3]{32}$$ = $$2 \sqrt[3]{4}$$

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Re: A certain clay cube has volume 64 cubic inches. If a smaller   [#permalink] 30 Sep 2017, 21:48
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