surface area question

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Intern

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surface area question [#permalink]

17 Sep 2007, 22:27

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. :cry:

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[#permalink]

17 Sep 2007, 22:43

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%

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Re: surface area question [#permalink]

18 Sep 2007, 00:19

chronolinkz wrote:

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%

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thksss [#permalink]

18 Sep 2007, 08:20

thanks so much for ur explanations.... it definitely clarifies everything. i really appreciate it. one down, many more to go.....lol

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Re: surface area question [#permalink]

21 Oct 2007, 20:32

chronolinkz wrote:

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%

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Re: surface area question [#permalink]

21 Oct 2007, 20:48

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, 20:48

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