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# geometry_cube

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Director
Joined: 22 Aug 2007
Posts: 566

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14 Oct 2007, 00:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

thanks.
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VP
Joined: 08 Jun 2005
Posts: 1145

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14 Oct 2007, 01:07
You can put 64 1cm cubes into 4cm cube. since 4^3 = 64 and 1^3 = 1.

64/1 = 64

the surface area of 4cm cube is 4^2*6 = 96. the surface area of 1cm cube is 1^2*6 = 6 but we have 64 cubes.

64*6/96 = 4 = 400%

SVP
Joined: 01 May 2006
Posts: 1796

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14 Oct 2007, 01:20
KillerSquirrel wrote:
You can put 64 1cm cubes into 4cm cube. since 4^3 = 64 and 1^3 = 1.

64/1 = 64

the surface area of 4cm cube is 4^2*6 = 96. the surface area of 1cm cube is 1^2*6 = 6 but we have 64 cubes.

64*6/96 = 4 = 400%

I agree on all, except the conclusion.

% Increase = 100 * (New surface - Old surface) / Old Surface = 100 * (64*6 - 96) / 96 = 300 %

So (D) for me
Director
Joined: 22 Aug 2007
Posts: 566

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14 Oct 2007, 11:49
Thank you for explanations, KS!

AO is D.

4-1=300% increase
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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15 Oct 2007, 12:31
IrinaOK wrote:
Thank you for explanations, KS!

AO is D.

4-1=300% increase

what is the reasoning behind this?
Director
Joined: 22 Aug 2007
Posts: 566

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15 Oct 2007, 12:37
KillerSquirrel wrote:
You can put 64 1cm cubes into 4cm cube. since 4^3 = 64 and 1^3 = 1.

64/1 = 64

the surface area of 4cm cube is 4^2*6 = 96. the surface area of 1cm cube is 1^2*6 = 6 but we have 64 cubes.

64*6/96 = 4 = 400%

PLUS to the KS explanation,

(64*6 - 96) / 96 = 4-1 = 3 we are speaking about percentage so multiply by 100%, we get 300 %.

we need to deduct one, cuz the stem is asking percentage increase.
Director
Joined: 31 Mar 2007
Posts: 576

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15 Oct 2007, 16:43
D

remember this when doing this question

sides in a cube = 6

4x4 = 16 per side x 6 = 96 sq cm

now just draw some pictures and you can figure out you can get 64 cubes, each having sides 1 sq cm, times 6 = 6

so new surface area is 384 - 96 = 288 / 96 = 3 x 100% = 300%.

D
15 Oct 2007, 16:43
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