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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]

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12 Feb 2012, 20:33
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Question Stats:

61% (02:03) correct 39% (00:50) wrong based on 254 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
[Reveal] Spoiler: OA

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Re: Surface area of a cube [#permalink]

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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.

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

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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.

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

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

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27 May 2013, 04:51
Bumping for review and further discussion.
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Re: What is the ratio of the surface area of a cube to the [#permalink]

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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.

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]

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22 Jun 2013, 02:31
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.

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]

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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]

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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]

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

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

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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.

Is this clear?

Cheers!
J

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

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27 Jan 2015, 14:38
Assume the length is Y

Surface are of Cube= 6Y^2

As the length is doubled for rectangle , other remains same. That means, rectangle's width,and height is "Y" but it's length is "2Y" now.

Let's see the surface area of Rectangle

Length = 2Y
Width = Y
Height = Y

So,
Multiplying length with height, 2Y x Y = 2Y^2 . Since there are two sides then it will be multiplied by two. So it will be 4Y^2

Multiplying length with width, 2Yx Y = 2Y^2 .Now multiply with two and we get 4Y^2

Multiplying Width with height, Y x Y = Y^2 Now multiply with two and we get 2Y^2

After Adding them , 4Y^2+4Y^2+2Y^2 = 10Y^2

Now,
6y^2/10Y^2 = 3/5
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Re: What is the ratio of the surface area of a cube to the surfa [#permalink]

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27 Jan 2015, 21:15
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. 1/4
B. 3/8
C. 1/2
D. 3/5
E. 2

Another way to think about it:

Imagine the cube with 6 equal faces. The surface area will be 6s^2 (s is the length of the edge of the cube).
Now imagine pulling on one face of the cube to elongate it. Now you have 4 extra equal faces on the four sides. The extra surface area is 4s^2.

Ratio of surface area of cube:surface area of rectangular solid = 6:10 = 3:5

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Re: What is the ratio of the surface area of a cube to the surfa   [#permalink] 25 Nov 2015, 14:38
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