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# The ratio of the volume of cube A to the volume of cube B is 1 to

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
The ratio of the volume of cube A to the volume of cube B is 1 to  [#permalink]

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17 Sep 2018, 20:57
00:00

Difficulty:

55% (hard)

Question Stats:

53% (02:10) correct 47% (02:16) wrong based on 30 sessions

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The ratio of the volume of cube A to the volume of cube B is 1 to $$3\sqrt{3}$$. If the diagonal of cube A is 10, what is the area of a face of cube B?

A. 10

B. 100/3

C. $$30\sqrt{3}$$

D. 100

E. $$300\sqrt{3}$$

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Re: The ratio of the volume of cube A to the volume of cube B is 1 to  [#permalink]

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18 Sep 2018, 00:15
Bunuel wrote:
The ratio of the volume of cube A to the volume of cube B is 1 to $$3\sqrt{3}$$. If the diagonal of cube A is 10, what is the area of a face of cube B?

A. 10

B. 100/3

C. $$30\sqrt{3}$$

D. 100

E. $$300\sqrt{3}$$

Ratio of Volume = (Ratio of Sides)^3

Given, Ratio of Volumes of A and B = 1/3√3 = 1/√27 = (Ratio of Sides)^3

i.e. Ratio of Sides = 1/√3
i.e. Diagonal of cube A / Diagonal of Cube B = 1/√3
i.e. Diagonal of Cube B = 10√3 = Side√3
i.e. Side of Cube B = 10
i.e. Area of face of Cube B = 10^2 = 100

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Re: The ratio of the volume of cube A to the volume of cube B is 1 to  [#permalink]

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18 Sep 2018, 02:14
Bunuel wrote:
The ratio of the volume of cube A to the volume of cube B is 1 to $$3\sqrt{3}$$. If the diagonal of cube A is 10, what is the area of a face of cube B?

A. 10

B. 100/3

C. $$30\sqrt{3}$$

D. 100

E. $$300\sqrt{3}$$

VA:VB = 1: 3\sqrt{3}
let cube A & B have sides a & b resp.
=> \sqrt{3}a = 10
=> a = 10/\sqrt{3}
=> VA = 1000/(\sqrt{3})^3
Since VA:VB = 1:3\sqrt{3} , multiply by 1000/(\sqrt{3})^3
VB becomes 1000
=> b = 10
hence, surface area = 10*10 = 100
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Joined: 09 Sep 2018
Posts: 1
Re: The ratio of the volume of cube A to the volume of cube B is 1 to  [#permalink]

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21 Sep 2018, 07:01
For the diagonal of cube A it is meant the space diagonal or the face diagonal?

Re: The ratio of the volume of cube A to the volume of cube B is 1 to &nbs [#permalink] 21 Sep 2018, 07:01
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