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by gmatmachoman » Wed Apr 21, 2010 1:39 am
A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal
cubes. What is the ratio of the surface area of the smallest cube as a percentage of the original
cube ?


1] 1/16

2] 1/64

3] 1/256

4] 1/4
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by liferocks » Wed Apr 21, 2010 1:45 am
vol of big cube length of side area of surface
a^3 a 6a^2
a^3/64 a/4 6a^/16

hence ratio of small to big 1/16
1 question...do you want the ratio of the percentage.in the second case smalles cube will have surface wich is 100/16 % or 6.25% of the large one

option 1
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by kstv » Wed Apr 21, 2010 1:47 am
Let dimesion of original cube be 4 x 4 x 4 = 64

surfaces area = 6 X 4 X 4

smallest cube will be 1 x 1 x 1

surface area = 6

Ratio = 6/6*16 = 1/16
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by ajith » Wed Apr 21, 2010 1:47 am
gmatmachoman wrote:A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal
cubes. What is the ratio of the surface area of the smallest cube as a percentage of the original
cube ?


1] 1/16

2] 1/64

3] 1/256

4] 1/4
The smallest cube will have 1/4 the side of the big cube as side
The suface area will be = 6*1/4a*1/4 a = 6a^2/16
The surface area of the big cube = 6a^2
ratio = 1/16
[spoiler]1) [/spoiler]
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by pops » Wed Apr 21, 2010 1:57 am
When you make 8 cubes from 1 imagine you divide one cube in two parts and each part is then divided in 4. Hence, each side of the smaller cubes is 1/2 of original cube.
So after second division into further 8 cubes sides are reduced to 1/4

surface area of cube=6*side^2
hence ratio = 1/16
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by gmatmachoman » Wed Apr 21, 2010 2:04 am
Thanks guys!!
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by gmatmachoman » Wed Apr 21, 2010 2:05 am
ajith wrote:
gmatmachoman wrote:A cube is divided into 8 equal cubes. Each of these cubes is further sub-divided into 8 equal
cubes. What is the ratio of the surface area of the smallest cube as a percentage of the original
cube ?


1] 1/16

2] 1/64

3] 1/256

4] 1/4
The smallest cube will have 1/4 the side of the big cube as side
The suface area will be = 6*1/4a*1/4 a = 6a^2/16
The surface area of the big cube = 6a^2
ratio = 1/16
[spoiler]1) [/spoiler]
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by akhpad » Wed Apr 21, 2010 3:00 am
I am fine with the above solution.

But I have one Q.

What is the ratio of the surface area of the smallest cube as a percentage of the original cube ?

What is the role of percentage over here? Above all choices given in ratio only.
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