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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gmatmachoman
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liferocks
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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
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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ajith
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The smallest cube will have 1/4 the side of the big cube as sidegmatmachoman 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 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]
Always borrow money from a pessimist, he doesn't expect to be paid back.
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
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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gmatmachoman
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gmatmachoman
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Ajith bhai..ajith wrote:The smallest cube will have 1/4 the side of the big cube as sidegmatmachoman 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 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]
Congrats for your 100 th Thx!! I missed thanking u as the 100 th guy..but 101 is also a nice figure!!
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akhpad
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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.
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.
