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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
What is the volume of a cube whose surface area is twice that of a cub  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 64% (01:29) correct 36% (01:13) wrong based on 28 sessions

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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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Joined: 27 Sep 2018
Posts: 37
Re: What is the volume of a cube whose surface area is twice that of a cub  [#permalink]

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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]

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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

volume =1 ; side = 1
TSA = 6
twice TSA = 6*2 ; 12
so side 6*s^2 = 12
s= 2√2
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Re: What is the volume of a cube whose surface area is twice that of a cub  [#permalink]

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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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: What is the volume of a cube whose surface area is twice that of a cub   [#permalink] 29 Mar 2019, 07:47
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