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

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A 4 cm cube is cut into 1 cm cubes. What is the percentage [#permalink] New post 09 Nov 2006, 04:43
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in area in the surface area after such cutting?

4%
166%
266%
300%
400%





Could you pls explain the answer also .
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 [#permalink] New post 09 Nov 2006, 05:00
The volume of the first cube is: 4x4x4=64m3
The surface area of this cube is 4x4x6=96m2

If you want to break this cube down to 1cm per side cubes, you get 64 such cubes.

The total suface aread of these cubes is 64x1x1x6=384m2

384 is 4 times 96 which means that in increases by 300%. D
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D [#permalink] New post 09 Nov 2006, 09:03
Area of cube = 6a*a

Original = 6*4*4= 96cm^2

Smaller cube area = 6*1*1=6cm^2
There are 64 smaller cube total area of small cubes 6*64=384

% increase =
(Area of smaller cube - area of large cube) / area of large cube =
(384-96)*100/96=288*100/96= 300%
D   [#permalink] 09 Nov 2006, 09:03
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