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# If a 4 cm cube is cut into 1 cm cubes, then what is the

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If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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15 Jan 2011, 15:07
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Difficulty:

55% (hard)

Question Stats:

64% (01:56) correct 36% (02:11) wrong based on 583 sessions

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If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

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

Please can someone explain this problem better.
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Joined: 02 Sep 2009
Posts: 50003
Re: surface area of cube  [#permalink]

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15 Jan 2011, 15:34
4
4
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

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Re: surface area of cube  [#permalink]

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15 Jan 2011, 17:19
generally you have at least two ways to solve a question......this mean that we should have different points of view to tackle a problem, right ??'

rethoric question I guess ........
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Re: surface area of cube  [#permalink]

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15 Jan 2011, 22:04
Hi,

when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64

Thanks

Bunuel wrote:
Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

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Re: surface area of cube  [#permalink]

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16 Jan 2011, 02:55
rohu27 wrote:
Hi,

when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64

Thanks

Bunuel wrote:
Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

The big cube which dimensions 4*4*4 can "produce" 4*4*4 small cubes with dimensions of 1*1*1 (base layer can give 4*4 small cubes and as there are 4 layers than total of 4*4*4 small cubes).
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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04 Mar 2014, 04:09
1
Big cube surface area = 4*4*6 = 96

Small cubes surface area (Total) = 6 *64

% = 6*64*96/100 = 400

% Increase = 400-100 = 300% = Answer = D
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Re: surface area of cube  [#permalink]

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04 Mar 2014, 04:15
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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13 Aug 2014, 04:08
I have problem with its verbal... 4cm cube! Does it mean that each side is 4cm or the area is 4cm...? is it popular to use this language in Geometry?
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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13 Aug 2014, 06:40
amirsalehi wrote:
I have problem with its verbal... 4cm cube! Does it mean that each side is 4cm or the area is 4cm...? is it popular to use this language in Geometry?

The area cannot be in units, it's in square units, so 4cm can only mean length of something.
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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23 Nov 2014, 12:58
1
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

Hey Bunuel,

My question might sound stupid but why are you going back and calculating the volume of the bigger cube. Why can't we just take the the side to be 1 and hence the surface area=6a^2=6. What is wrong with my thinking
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Posts: 50003
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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24 Nov 2014, 06:37
davidfrank wrote:
Bunuel wrote:
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

4%
166%
266%
300%
400%

Please can someone explain this problem better.

Cube has 6 faces. The surface area of a cube which has a side of 4cm is 6*4^2=6*16 cm^2.

Now, when the cube is cut into the smaller cubes with side of 1cm we'll get 4*4*4=64 little cubes and each will have the surface area equal to 6*1^2=6 cm^2, so total surface are of these 64 little cubes will be 6*64 cm^2.

6*64 is 4 times more than 6*16 which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): $$Percent=\frac{Change}{Original}*100$$

So the percent increase will be: $$Percent=\frac{Change}{Original}*100=\frac{6*64-6*16}{6*16}*100=300%$$.

Hey Bunuel,

My question might sound stupid but why are you going back and calculating the volume of the bigger cube. Why can't we just take the the side to be 1 and hence the surface area=6a^2=6. What is wrong with my thinking

When a cube with a side of 4 units is cut into cubes with a side of 1 unit you get 64 little cubes. Each of them will have the surface area of 6 square units, thus the surface area of all 64 little cubes will be 6*64 square units.
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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04 Apr 2018, 04:20
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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04 Apr 2018, 10:21
hdavies wrote:
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300

What would you get with your approach if the big cube were cut into 2cm cubes, instead of 1cm cubes?
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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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04 Apr 2018, 10:47
ajit257 wrote:
If a 4 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

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

Please can someone explain this problem better.

6×4×4 = 96 cubic cm

Totally #64 1cm cubes which equals 64×6 = 384 cubic cm

Percent increase = 382-96/96 * 100
= 288*100/96
= 300

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Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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04 Apr 2018, 15:42
Bunuel wrote:
hdavies wrote:
Hi Bunuel

Is it a coincidence (or luck) that this problem can be solved by ignoring the fact that we are asked to solve for the percent difference in surface area? We have something that is 4 times something else. What's the percent change?

((4-1)/1) *100 = 300

What would you get with your approach if the big cube were cut into 2cm cubes, instead of 1cm cubes?

I see. The approach I mentioned above would show 100% change, but the real answer would be undefined I think.
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the &nbs [#permalink] 04 Apr 2018, 15:42
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