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

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What is the ratio of the surface area of a cube to the surfa [#permalink] New post 12 Feb 2012, 20:33
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (02:01) correct 37% (00:51) wrong based on 126 sessions
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
[Reveal] Spoiler: OA

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Re: Surface area of a cube [#permalink] New post 12 Feb 2012, 20:41
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Let X be the side of the cube. Therefore X^2*6= surface area.

the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.

6X^2/10X^2 = 3/5.

Answer = D
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Re: What is the ratio of the surface area of a cube to the [#permalink] New post 13 Feb 2012, 05:25
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enigma123 wrote:
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)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?


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.

Answer: D.
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Re: What is the ratio of the surface area of a cube to the [#permalink] New post 23 Feb 2012, 05:57
surface area of Cube = 6sidesqr
surface area of rectangular soild = 2( lb + bh+ hl)
assume side of cube is X
its surface area is 6Xsqr
surface area of Recatngular solid is = 10Xsqr ( 2( 2Xsqr+Xsqr +2Xsqr))
take ratio of these two we will get 6/10 = 3/5
Answer D
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Re: What is the ratio of the surface area of a cube to the [#permalink] New post 27 May 2013, 04:51
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Re: What is the ratio of the surface area of a cube to the [#permalink] New post 22 Jun 2013, 00:56
Bunuel wrote:
enigma123 wrote:
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)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?


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.

Answer: D.


why "4+4+2" if there are two cubes than it should be "4+4" = 8 faces
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Re: What is the ratio of the surface area of a cube to the [#permalink] New post 22 Jun 2013, 02:31
Expert's post
WarriorGmat wrote:
Bunuel wrote:
enigma123 wrote:
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)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?


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.

Answer: D.


why "4+4+2" if there are two cubes than it should be "4+4" = 8 faces


Plus 2 faces on the top and bottom. Put two dice one on another and see how many faces will it have.
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Re: What is the ratio of the surface area of a cube to the surfa [#permalink] New post 14 Nov 2013, 19:12
\frac{6S^2}{2(lb+bh+hl)}=\frac{6x^2}{2(2x^2+x^2+2x^2)}=\frac{6x^2}{10x^2}=\frac{3}{5}
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Re: What is the ratio of the surface area of a cube to the surfa [#permalink] New post 14 Nov 2013, 19:17
Do not get confused as to why I took x. Let side of the cube be x. He says length is doubled. So, l=2x. However, b and h remain unchanged. So, b=h=x.
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Re: What is the ratio of the surface area of a cube to the surfa [#permalink] New post 27 Mar 2014, 01:09
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Area of cube = a^2 + a^2 + a^2 + a^2 + a^2 + a^2 = 6 a^2

When one of the dimension is doubled, it has impact on 4 sides (rest 2 remains same)

Look at the diagram

Area of rectangular solid = a^2 + a^2 + 2 a^2 + 2 a^2 + 2 a^2 + 2 a^2 = 10 a^2

Ratio = \frac{6 a^2}{10 a^2} = \frac{3}{5}

Answer = D
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Re: What is the ratio of the surface area of a cube to the surfa [#permalink] New post 31 Mar 2014, 07:35
Hi All,

Let's assume leg of cube is 1 then surface area will be 6(1)^2=6. Now, rectangular solid will be (2)(1)(1), The area of the solid 2(ab+ac+bc) where a=2, b=1 and c=1. Thus its surface area totals 2(5)=10. So then D, 6/10=3/5 is the surface area.

D is the correct answer

Is this clear?

Cheers!
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Re: What is the ratio of the surface area of a cube to the surfa   [#permalink] 31 Mar 2014, 07:35
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