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# What is the ratio of the surface area of a cube to the surfa

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SVP
Joined: 04 May 2006
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What is the ratio of the surface area of a cube to the surfa [#permalink]

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04 Mar 2008, 00:26
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45% (medium)

Question Stats:

56% (01:51) correct 44% (00:46) wrong based on 191 sessions

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What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A. 1/4
B. 3/8
C. 1/2
D. 3/5
E. 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-ratio-of-the-surface-area-of-a-cube-to-the-surfa-127459.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Mar 2014, 01:08, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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05 Mar 2008, 21:41
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One side surface area of a cube = x*x = x^2
Total 6 sides = 6x^2

As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.
L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2
W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2
Total 6 sides = 8x^2 + 2x^2 = 10x^2

Ratio of cube area to rectangular area = 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (E)
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Jimmy Low, Frankfurt, Germany
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Re: What is the ratio of the surface area of a cube to the [#permalink]

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26 Mar 2014, 17:01

Guys,

Can some one draw this for me....

~M14
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Re: What is the ratio of the surface area of a cube to the [#permalink]

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27 Mar 2014, 01:10
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Expert's post
Mountain14 wrote:

Guys,

Can some one draw this for me....

~M14

What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A. 1/4
B. 3/8
C. 1/2
D. 3/5
E. 2

30 second approach:
A cube has 6 faces, suppose each has an area of 1, so surface area of the cube will be 6;

A rectangular solid identical to the cube in all ways except that its length has been doubled is just complicated way of saying that the rectangular solid is built with two cubes, hence it has 4+4+2=10 faces of a little cube (just imagine to cubes put one on another) and thus the surface area of the rectangular solid will be 10;

Ratio: 6/10=3/5.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-ratio-of-the-surface-area-of-a-cube-to-the-surfa-127459.html
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Re: What is the ratio of the surface area of a cube to the   [#permalink] 27 Mar 2014, 01:10
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