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

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Difficulty:   45% (medium)

Question Stats: 64% (01:37) correct 36% (01:18) wrong based on 245 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

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

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4
4
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: Surface area of a cube  [#permalink]

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4
1
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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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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Posts: 43
Re: What is the ratio of the surface area of a cube to the  [#permalink]

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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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Joined: 02 Sep 2009
Posts: 58327
Re: What is the ratio of the surface area of a cube to the  [#permalink]

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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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$$\frac{6S^2}{2(lb+bh+hl)}$$=$$\frac{6x^2}{2(2x^2+x^2+2x^2)}$$=$$\frac{6x^2}{10x^2}$$=$$\frac{3}{5}$$
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Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

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

Attachments cub.jpg [ 22.23 KiB | Viewed 18246 times ]

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

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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?

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

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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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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]

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did it by knowing that surface area of a cube is always 6*side^2
since the rectangular has 2x as it's length and the rest is the same, we have:
2*(2x*x)+2(2x*x)+2x^2 = 10x^2

6x^2/10x^10 = 3/5
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

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Hi All,

This question can be solved by TESTing VALUES. You would likely find it helpful to physically draw the cube and solid.

Since the answer choices do not include variables, we can use whatever values we'd like for the dimensions of the cube and for the rectangular solid (as long as we follow the Facts described in the prompt). Given the one specific rule (the length of the rectangular solid is double the length of the cube), I'll TEST the easiest VALUES that I can think of...

Cube = (1)(1)(1)
Solid = (1)(1)(2)

Surface Area of Cube = 6(1) = 6
Surface Area of Solid = 2(1) + 4(2) = 10

Thus, the ratio of the two Surface Areas is 6:10 = 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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