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

Question

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}

GMATinsight · Answer

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

Answer:option D

thefibonacci · Answer

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

aleg · Answer

For the diagonal of cube A it is meant the space diagonal or the face diagonal?

Thank you for your help!

TheGuyDangerous · Answer

Given the diagonal of the cube A as 10. Diagonal = a\sqrt{3} = 10 => a=10/\sqrt{3}

Asper the ratio given, 1/3*\sqrt{3} = (10/\sqrt{3})^3 / A^3

Solving we get A as 10

Surface area = A^2 = 10^2 = 100

Ans D

anmol950915 · Answer

is this question still relevant for Gmat FE

Bunuel · Answer

Even though this question can be solved by applying the Pythagorean Theorem twice, first for the face and then for the space diagonal of the cube, I don’t think this kind of question is likely to show up on the GMAT anymore. (The Pythagorean Theorem itself is still tested on the GMAT, since it’s considered basic math knowledge rather than advanced or specialized geometry.)

P.S. Check these two topics:

GMAT Syllabus for Focus Edition  
  Geometry Tested on GMAT Focus?

While specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and the Pythagorean theorem are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

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

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