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# If a certain cube has Volume V and a second cube has twice

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Director
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If a certain cube has Volume V and a second cube has twice  [#permalink]

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09 Jan 2013, 21:07
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12
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Difficulty:

45% (medium)

Question Stats:

69% (01:51) correct 31% (02:01) wrong based on 444 sessions

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If a certain cube has Volume V and a second cube has twice the surface area of the first cube, what is the volume of the second cube in terms of V?

A. $$\sqrt{2}V$$
B. $$2\sqrt{2}V$$
C. 2V
D. 4V
E. 8V

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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11 Jan 2013, 04:46
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fozzzy wrote:
If a certain cube has Volume V and a second cube has twice the surface area of the first cube, what is the volume of the second cube in terms of V?

A. $$\sqrt{2}V$$
B. $$2\sqrt{2}V$$
C. 2V
D. 4V
E. 8V

Say the volume of the first cube is V=8, hence its side must be 2. Thus its surface area is 2^2*6=24.

The surface are of the second cube will be 48, which means that the are of a face is 48/6=8. So, the side is $$\sqrt{8}$$. The volume = $$(\sqrt{8})^3=16\sqrt{2}$$.

Now, plug V=8 into the answer choices and see which one yields $$16\sqrt{2}$$. Only option B fits.

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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09 Jan 2013, 22:16
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Let volume of cube be = 1
Surface area = 6
Surface area of 2nd cube = 12
Side of second cube = $$\sqrt{2}$$
Volume of second cube = $$2*\sqrt{2}$$

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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09 Jan 2013, 23:01
MacFauz wrote:
Let volume of cube be = 1
Surface area = 6
Surface area of 2nd cube = 12
Side of second cube = $$\sqrt{2}$$
Volume of second cube = $$2*\sqrt{2}$$

Everything is right I'm not sure how to write math functions here so A and B look similar, answer is B.
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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09 Jan 2013, 23:12
fozzzy wrote:
MacFauz wrote:
Let volume of cube be = 1
Surface area = 6
Surface area of 2nd cube = 12
Side of second cube = $$\sqrt{2}$$
Volume of second cube = $$2*\sqrt{2}$$

Everything is right I'm not sure how to write math functions here so A and B look similar, answer is B.

Oops.. Thanks for pointing that out.. Question formatted and answer changed..
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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10 Jan 2013, 08:14
Plug in actual numbers. Use 2 as the side of the first cube. Surface area would equal 24 and volume would equal 8. For the surface area for the 2nd cube to be double (48) the 1st cube we would have sides of 2root2 and a volume of 16root2.

Therefore 8 x ? = 16root2....this only leaves 2root2
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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10 Jan 2013, 19:31
MacFauz wrote:
Let volume of cube be = 1
Surface area = 6
Surface area of 2nd cube = 12
Side of second cube = $$\sqrt{2}$$
Volume of second cube = $$2*\sqrt{2}$$

I din't understand the side of the second cube...how do you derive a side from the Total Surface Area????
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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10 Jan 2013, 19:53
4112019 wrote:
MacFauz wrote:
Let volume of cube be = 1
Surface area = 6
Surface area of 2nd cube = 12
Side of second cube = $$\sqrt{2}$$
Volume of second cube = $$2*\sqrt{2}$$

I din't understand the side of the second cube...how do you derive a side from the Total Surface Area????

TSA of cube = 6a^2
volume = a^3

so he started with volume = 1 ( a=1)
then 6a^2 = 6 >>> first cube
then second cube = double that so its 12
6a^2 = 12, a^2 = 2 >> a = root 2

volume of second cube = a^3 = root 2 cubed so that's 2 root 2
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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11 Jan 2013, 00:21
Given the volume of first cube V, the side of the cube is V raised to 1/3. Surface area of the first cube (4 * side ^2) will be 4*V raised to 2/3

Let the side of the second cube be x. Given the surface of the second cube is twice the surface area of the first cube, the surface area of the second cube can be expressed as

4 * x^2 = 2*4 V raised to 2/3

x^2 = 2 * V raised to 2/3

x = sqrt(2) * V raised to 1/3

volume of second cube will be x^3 = 2sqrt2 * V

P.S. I interpreted surface area as the lateral surface area but not the total surface area; question would have specifically given if it was referring to total surface area and then the formula would have been 6 * side^2
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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11 Jan 2013, 05:14
2
first cube:
$$V = s^3$$
$$SA = 6*s^2$$

second cube:
$$SA = 12*s^2$$

get S:
$$side = \sqrt{2} s$$
$$V_2 = side ^ 3 = 2\sqrt{2}*s^3$$
$$V_2 = 2\sqrt{2}V$$

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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24 Jan 2013, 08:24
gmat dose not test the remembering of formular.

do not need formula

s=Ar^2
we infer R=r. roor square of 2
V=Br^3
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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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21 May 2014, 09:54
Moving along with the question

Volume of first Cube = V
side = V^(1/3)
surface area = 6* V^(2/3)

Surface area of 2nd cube = 2* 6 * V^(2/3) = 12*V^(2/3)
side = sqrt (surface area /6) =sqrt (2V^(2/3)) = sqrt(2) * V^(1/3)
Volume = side^3 = [sqrt(2) * V^(1/3)]^3
= 2*sqrt(2)* V

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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22 May 2014, 23:51
2
First Cube details

Let the side = a

Volume $$V = a^3$$

Surface area $$= a^2$$

Second Cube details

Given that Surface area is twice $$= 2a^2$$

It means each side is $$\sqrt{2}a$$

So volume would be $$\sqrt{8} a^3 = 2\sqrt{2} . V$$

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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20 Jul 2017, 16:36
fozzzy wrote:
If a certain cube has Volume V and a second cube has twice the surface area of the first cube, what is the volume of the second cube in terms of V?

A. $$\sqrt{2}V$$
B. $$2\sqrt{2}V$$
C. 2V
D. 4V
E. 8V

Since the first cube has a volume of V, V = s^3, where s = the side of the cube; thus, s = ∛V.

Since a cube has 6 faces, the surface area of the first cube is 6(∛V)^2 and thus the surface area of the second cube, which is twice that of the first cube, is 12(∛V)^2.

We can let S = the side of the second cube; thus:

6S^2 = 12(∛V)^2

S^2 = 2(∛V)^2

S = √2 * ∛V

Therefore, the volume of the second cube is S^3 = (√2 * ∛V)^3 = (√2)^3 * V = (√2)^2 * √2 * V = 2√2V.

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Re: If a certain cube has Volume V and a second cube has twice  [#permalink]

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21 Jul 2018, 06:13
fozzzy wrote:
If a certain cube has Volume V and a second cube has twice the surface area of the first cube, what is the volume of the second cube in terms of V?

A. $$\sqrt{2}V$$
B. $$2\sqrt{2}V$$
C. 2V
D. 4V
E. 8V

Let's say side of first cube is a and side of second cube is $$x$$

$$a^3$$= V
$$a= V^1^/^3$$

Surface Area of first cube $$=$$ $$6*a^2$$ $$=$$ $$6*V^2^/^3$$
Surface Area of Second Square $$=6*x^2$$

Now Equate as per question

$$6*x^2= 2*6*V^2^/^3$$
$$x=2^2*V^1^/^3$$

Volume second square $$= X^3$$ $$=2*\sqrt{2}*V$$
Re: If a certain cube has Volume V and a second cube has twice &nbs [#permalink] 21 Jul 2018, 06:13
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