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

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Director
Joined: 16 May 2007
Posts: 548
What is the ratio of the surface area of a cube to the [#permalink]

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12 Aug 2007, 05:18
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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
Senior Manager
Joined: 04 Jun 2007
Posts: 345
Re: PS : Ratio of surface areas [#permalink]

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12 Aug 2007, 05:30
trahul4 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

This one should be D.

Surface area cube1 = 6*a^2
Surface area cube2 = 2*(a^2 + 2a*a + 2a*a) = 10*a^2
So, ratio is 3/5.
Senior Manager
Joined: 04 Jun 2007
Posts: 345
Re: PS : Ratio of surface areas [#permalink]

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12 Aug 2007, 06:11
trahul4 wrote:
sumande wrote:
Surface area cube2 = 2*(a^2 + 2a*a + 2a*a) = 10*a^2
.

can you tell me how you arrived at this ?

If each side of the original cube is a, then for the new cube the sides will be 2a, a, a.
Four faces of the new cube will have an area 2a*a and the remaining two faces have area a*a.
Surface area of a cuboid (rectangular solid) = 2(lb + lh + bh), where l,b,h are respectively the length, breadth and height of the solid.
Intern
Joined: 09 Aug 2007
Posts: 33

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12 Aug 2007, 06:15
the rectangular solid has 6 sides - 2 of which are squares, 4 of which are rectangles. you can pick numbers to illustrate:

cube with sides of length 4: area = (4*4)(6) = 96

rectangular solid with dimensions 8 x 4 x 4 (the only dimension that changes is the length, which is doubled) still has six sides, but this time only 2 of them are still squares, the other 4 are rectangles:

(4*4)(2 sides) = 32
(8*4)(4 sides) = 128
total surface area of rectangular solid = 160

96/160 = 3/5
Director
Joined: 11 Jun 2007
Posts: 914
Re: PS : Ratio of surface areas [#permalink]

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12 Aug 2007, 08:39
trahul4 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

l = length, w = width, h = height
surface area = 2 (lw + wh + lh)

I just plugged in values to calculate what the ratio would be:

SA of square: l=w=h = 2
2 (2*2 + 2*2 + 2*2) = 24

SA of rectangle: l = 4, w=h = 2
2 (4*2 + 2*2 + 4*2) = 40

24/40 = 3/5 (D)
Intern
Joined: 08 Aug 2007
Posts: 2

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12 Aug 2007, 10:23
IMO D

Original Surface Area = 6a^2
New Surface Area = 10a^2

ratio - 3:5
Director
Joined: 16 May 2007
Posts: 548

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13 Aug 2007, 10:04
OA is ofcourse 3/5. Was easy eh ?
13 Aug 2007, 10:04
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