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What is the volume of a cube whose surface area is twice that of a cub

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Bunuel
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What is the volume of a cube whose surface area is twice that of a cub [#permalink] New post  27 Mar 2019, 00:15
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What is the volume of a cube whose surface area is twice that of a cube with volume 1?

(A) \(\sqrt{2}\)
(B) 2
(C) \(2\sqrt{2}\)
(D) 4
(E) 8
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itsanujsingh
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Re: What is the volume of a cube whose surface area is twice that of a cub [#permalink] New post  27 Mar 2019, 00:47
volume of cube= a^3=1
means a=1
surface area = 6 a^2= 6

Surface area of the cube whose surface area is twice of the cube of volume 1 =12
side==>6b^2=12
b=rt2

volume = b^3=(rt2)^3=2rt2
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Re: What is the volume of a cube whose surface area is twice that of a cub [#permalink] New post  27 Mar 2019, 02:54
Bunuel wrote:
What is the volume of a cube whose surface area is twice that of a cube with volume 1?

(A) \(\sqrt{2}\)
(B) 2
(C) \(2\sqrt{2}\)
(D) 4
(E) 8


volume =1 ; side = 1
TSA = 6
twice TSA = 6*2 ; 12
so side 6*s^2 = 12
s= 2√2
IMO C
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ScottTargetTestPrep
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Re: What is the volume of a cube whose surface area is twice that of a cub [#permalink] New post  29 Mar 2019, 07:47
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Bunuel wrote:
What is the volume of a cube whose surface area is twice that of a cube with volume 1?

(A) \(\sqrt{2}\)
(B) 2
(C) \(2\sqrt{2}\)
(D) 4
(E) 8


The side of a cube with a volume of 1 is ∛1 = 1, so the surface area is:

6 x 1^2 = 6

Thus, the other cube has a surface area of 12; solving for the side, we have:

6s^2 = 12

s^2 = 2

s = √2

Thus, the volume of the cube is √2 x √2 x √2 = 2√2.

Answer: C
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Re: What is the volume of a cube whose surface area is twice that of a cub [#permalink] New post  19 Aug 2023, 06:44
What is the volume of a cube whose surface area is twice that of a cube with volume 1?

Let us assume the side of new cube b a
Therefore,

=>6a^2 = 2*6*1^2
=> a = (2)^0.5

Volume of cube = a^3 = [(2)^0.5]^3 = 2(2)^0.5

Answer C
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Re: What is the volume of a cube whose surface area is twice that of a cub [#permalink]
19 Aug 2023, 06:44
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