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

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Senior Manager
Joined: 05 Jun 2005
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A 4 cm cube is cut into 1 cm cube. What is the percentage [#permalink]  19 Oct 2006, 16:09
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A 4 cm cube is cut into 1 cm cube. What is the percentage increase in the surface area after such cutting?

A) 4 %
B) 166%
C) 266%
D) 300%
E) 400%

Manager
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A 4 cm cube has a surface area of 96 square cm. (4x4x6 sides)

It would then be split into 64 1 cm cubes.

Each 1 cm cube would have a surface area of 6 square cm (1x1x6) for a total surface area of 64x6 = 384 square cm

(384 - 96) / 96 = 300%

Senior Manager
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burningskulls wrote:
A 4 cm cube has a surface area of 96 square cm. (4x4x6 sides)

It would then be split into 64 1 cm cubes.

Each 1 cm cube would have a surface area of 6 square cm (1x1x6) for a total surface area of 64x6 = 384 square cm

(384 - 96) / 96 = 300%

Thanks a ton burningskull, your explaination is a lot clearer than the OE
Director
Joined: 23 Jun 2005
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E
When you cut a cube with 4cm side into cubes with sides 1cm each, you will get 64 such cubes.
Surface area of one cube with side 1cm = 6sqcm.

For 64 cubes = 384 sqcm

Surface area of one cube with side 4cm = 96 sqcm

% increase = 384*100/96 = 400
Senior Manager
Joined: 23 May 2005
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Probably a stupid question but where did you get 64? How do you know that it can be cut up to 64 1 cm cubes?
Senior Manager
Joined: 01 Oct 2006
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The total volume should remain the same
Volume of 4cm cube is 64
Volume of 1 cm cube is 1
Thus we need to have 64 1 cm cubes

Surface area of 4 cm is cube 6*16=96
Surface area of 64 1 cm cubes is =64*1*6=384

percentage increase =(384-96)/96 *100=300

Senior Manager
Joined: 30 Aug 2006
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Agree D.

Hermione, think of a 2D grid 4 by 4 then split this up into increments of 1 on each axis, will give you 16. Then these 16 blocks are 4 high (as the height of the cube is 4), so 4*16 = 64.
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