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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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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?

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;

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 Answer D

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.

Answer: D.

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

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.
_________________

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.

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

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

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22 Nov 2015, 09:57

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

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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