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

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A certain clay cube has volume 64 cubic inches. If a smaller [#permalink] New post 07 Feb 2014, 15:47
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89% (01:43) correct 11% (00:45) wrong based on 46 sessions
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}
[Reveal] Spoiler: OA
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Re: How do you solve this [#permalink] New post 09 Feb 2014, 20:21
Expert's post
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.

You can solve for y to get your answer.
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A certain clay cube has volume 64 cubic inches. [#permalink] New post 19 May 2014, 09:07
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 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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Re: A certain clay cube has volume 64 cubic inches. [#permalink] New post 19 May 2014, 09:47
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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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Re: A certain clay cube has volume 64 cubic inches. [#permalink] New post 19 May 2014, 22:55
Expert's post
holdem 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 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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Re: A certain clay cube has volume 64 cubic inches. If a smaller [#permalink] New post 21 May 2014, 09:27
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)

Hence Answer is E
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Re: A certain clay cube has volume 64 cubic inches. If a smaller   [#permalink] 21 May 2014, 09:27
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