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Re: If a certain cube has Volume V and a second cube has twice
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11 Jan 2013, 03:46
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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.
Re: If a certain cube has Volume V and a second cube has twice
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10 Jan 2013, 07:14
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
Re: If a certain cube has Volume V and a second cube has twice
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10 Jan 2013, 23:21
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
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
Re: If a certain cube has Volume V and a second cube has twice
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20 Jul 2017, 15:36
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.
Answer: B
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