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# surface area question

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Intern
Joined: 11 Jul 2007
Posts: 26
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surface area question [#permalink]  17 Sep 2007, 21:27
guys, this is straight from the challenge set and i am not following with the explanation. i am so lost with their answer.

a 4 cm cube is cut into 1 cm cubes. what is the percentage increase in the surface area after such cutting?

4%
166%
266%
300%
400%

if you have the challenge set, please refer to question 11 of challenge 1.
i would appreciate if any of you guys can provide insight on this question. and to make matters worst this is just on of the many questions i don't get. its gonna be a longggg month of studying.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5077
Location: Singapore
Followers: 22

Kudos [?]: 186 [0], given: 0

[#permalink]  17 Sep 2007, 21:43
Surface area of 4*4*4 cube = (4*4)*6 = 96 cm^2

# of 1cm^3 cubes that can be cut = 64

Each cube has a surface area of 6cm^2 and 64 cubes will have surface area of 384 cm^2.

Increase in surface area = 384-96 = 288cm^2
% increase = 288/96 * 100% = 300%
Director
Joined: 09 Aug 2006
Posts: 765
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Kudos [?]: 72 [0], given: 0

Re: surface area question [#permalink]  17 Sep 2007, 23:19
chronolinkz wrote:
guys, this is straight from the challenge set and i am not following with the explanation. i am so lost with their answer.

a 4 cm cube is cut into 1 cm cubes. what is the percentage increase in the surface area after such cutting?

4%
166%
266%
300%
400%

if you have the challenge set, please refer to question 11 of challenge 1.
i would appreciate if any of you guys can provide insight on this question. and to make matters worst this is just on of the many questions i don't get. its gonna be a longggg month of studying.

The key thing to figure out in this question is that one 4cm cube will be cut into sixty four 1cm cubes to have the same volume, as shown below:

Vol of 1 cube with s 4cm = s^3 = 4*4*4 = 64
Therefore, 64 such cubes of s=1cm are required to have the same volume

Once you figure this out it's simple:
SA of one 4cm cube = 6*4*4
SA of 64 1cm cubes = 64*1*1 = 6*4*4*4

% inc. = [(6*4*4*4)-(6*4*4)]/(6*4*4) * 100
= [6*4*4(4-1)]/6*4*4 *100 = 300%
Intern
Joined: 11 Jul 2007
Posts: 26
Followers: 0

Kudos [?]: 1 [0], given: 0

thksss [#permalink]  18 Sep 2007, 07:20
thanks so much for ur explanations.... it definitely clarifies everything. i really appreciate it. one down, many more to go.....lol
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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Kudos [?]: 355 [0], given: 4

Re: surface area question [#permalink]  21 Oct 2007, 19:32
chronolinkz wrote:
guys, this is straight from the challenge set and i am not following with the explanation. i am so lost with their answer.

a 4 cm cube is cut into 1 cm cubes. what is the percentage increase in the surface area after such cutting?

4%
166%
266%
300%
400%

if you have the challenge set, please refer to question 11 of challenge 1.
i would appreciate if any of you guys can provide insight on this question. and to make matters worst this is just on of the many questions i don't get. its gonna be a longggg month of studying.

Volume of LARGE CUBE = S cubed
=4^3
=64 cm squared

Surface Area of LARGER CUBE = area of one face * # of faces
= (4*4) 6
= 16*6 = 96 cm squared (squared because we have "two" metrics)

Surface Area of one SMALLER CUBE = area of one face * # of faces
=1^2 * 6
= 6 cm squared

Total surface area of ALL the small cubes = 64 *6= 384

384 - 96 = 288

increase / beginning = 288 / 96 = 3 = 300%
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 68 [0], given: 7

Re: surface area question [#permalink]  21 Oct 2007, 19:48
chronolinkz wrote:
a 4 cm cube is cut into 1 cm cubes. what is the percentage increase in the surface area after such cutting?

4%
166%
266%
300%
400%

= (64x6 - 6x16)/(6x16)
= 96 x 3 /96
= 3 or 300%
Re: surface area question   [#permalink] 21 Oct 2007, 19:48
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# surface area question

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