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

first cube:
\(V = s^3\)
\(SA = 6*s^2\)

second cube:
\(SA = 12*s^2\)

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

Answer: B

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 \(\sqrt{8} a^3 = 2\sqrt{2} . V\)

Answer = B

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

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

Answer is B

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.

Answer: B

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..

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

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

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

So B is the answer

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

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
we infer the answer.

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 \(= X^3\) \(=2*\sqrt{2}*V\)

Bunuel

Please advise when to take lateral surface area and total surface area.

let vol of cube 1 = 27
side = 3 and TSA = 6s^2 = 54
so for cube 2 = TSA = 108
so each side ; √18= 3√2
vol; 54√2
i.e option B [m]2\sqrt{2}V

Let call the length of each side of first cube = a. Given that surface area of second cube = 2 first cube. Means that area of one face of second cube = 2 x area of first cube.

S2 = 2S1 --> S2 = 2a^2 ---> Length of each side of second cube = Square root (2) x a
---> V2 = (Square root 2xa)^3 = B answer

V and surface area =\(6a^2\)
Surface area of 2nd cube=\(12a^2\)
surface area of one face=\(2a^2\)
Side of the face=\(\sqrt{2a}\)
Volume=\(2\sqrt{2a^3}\)
Volume=\(2[square_root]2V[/square_roo\)t]

Plug in numbers:

First cube:

Volume = \(s^3\)

Volume = \(2^3 = 8\)

Surface area = \(2*2 * 6 = 24\)

Second cube:

Surface area = 48

\(48/6\) = 8

side =\( 2\sqrt{2}\)

Volume = \( (2\sqrt{2})^3 = 16\sqrt{2}\)

\(\frac{16\sqrt{2}}{8} = 2\sqrt{2}V\)

Answer is B.