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# A 4 cm cube is cut into 1 cm cubes. What is the percentage

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Director
Joined: 10 Feb 2006
Posts: 657
A 4 cm cube is cut into 1 cm cubes. What is the percentage [#permalink]

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06 May 2008, 21:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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%

Surface area of a cube = 6 * a ^2 = 6 * 4 * 4 = 24 * 4 = 80 + 16 = 90

I'm stuck here.
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CEO
Joined: 17 May 2007
Posts: 2950

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06 May 2008, 22:25
I guess the first thing we want to find out is how many new cubes will we see. To quickly calculate that divide the total volume of the big cube by the total volume of the small cube :

$$4^3 / 1^3 = 64$$ new cubes
surface area of big cube = $$4^2 * 6 = 96 sqm$$
total surface area of new cubes = $$64 * 1^2 * 6 = 384 sqm$$
% increase = $$(384 - 96)/96 * 100 = 300%$$

is this right ?
Director
Joined: 05 Jan 2008
Posts: 687

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07 May 2008, 04:03
I agree with BSD's solution.

while searching I got the below formula for
finding different solutions for cubes..

If the cube of n*n*n cut into 1*1*1

Then

No of cubes no side painted = (n-2)*(n-2)*(n-2)
No of cubes exactly one side painted = (n-2)*(n-2)*6
No of cubes exactly two side painted = (n-2)*12
No of cubes exactly three side painted = 8

Using the above formula we have
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CEO
Joined: 29 Mar 2007
Posts: 2559

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07 May 2008, 05:59
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%

Surface area of a cube = 6 * a ^2 = 6 * 4 * 4 = 24 * 4 = 80 + 16 = 90

I'm stuck here.

I get . 4*4*6 = surface area of original cube.

We get 64 small cubes. the surface area of these 1cm cubes are 6cm^3.

Now its just 6*64 = 384.

We find the % increase by: (384-96)/96 =3 or 300%.
Current Student
Joined: 27 Mar 2008
Posts: 415
Schools: Kellogg Class of 2011

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07 May 2008, 06:33
Re: cube.   [#permalink] 07 May 2008, 06:33
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