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Interesting Geometry Question

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Interesting Geometry Question

by killerdrummer » Tue Mar 26, 2013 1:41 am
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

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


Although I have posted answer below but i am still looking for a quick and crisp method. :)

[spoiler]
-----------------------------------------------------------------------------------------------
D
-----------------------------------------------------------------------------------------------
Solution:

Volume of bigger cube(BC) = 4*4*4 = 64
Volume of Smaller CUBE (SC) = 1*1*1 = 1
Therefore we have 64 small cubes

SA = 6 (SIDE)*(SIDE) BC = 96 & SC =64*6= 384
%inc = [(384-96)/96]*100
[/spoiler]
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by Alina Ross » Tue Mar 26, 2013 2:35 am
The General solution would be as below:
Solution: 

Volume of bigger cube(BC) = 4*4*4 = 64 
Volume of Smaller CUBE (SC) = 1*1*1 = 1 
Therefore we have 64 small cubes 

SA = 6 (SIDE)*(SIDE) BC = 96 & SC =64*6= 384 
%inc = [(384-96)/96]*100
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by Anju@Gurome » Tue Mar 26, 2013 8:24 am
killerdrummer wrote:A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
Total surface area of a cube = (Number of faces)*(Surface area of a face) = 6a², where a is the length of each edge of the cube.

Total surface area of the 4cm cube = 6*(4²) = 6*16 sq. cm
Total surface area of the 1cm cube = 6*(1²) = 6 sq. cm

Number of 1cm cubes = (Volume of 4cm cube)/(Volume of 1cm cube) = 4³/1³ = 4³ = 64

Hence, required percentage = 100*(Total surface area of all the 1cm cubes - Total surface area of the 4cm cube)/(Total surface area of the 4cm cube) = 100*(6*64 - 6*16)/(6*16) = 100*(4 - 1)/1 = 100*3 = 300

The correct answer is D.
Anju Agarwal
Quant Expert, Gurome

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