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Manager  Joined: 28 Aug 2010
Posts: 154
If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 64% (01:56) correct 36% (02:13) wrong based on 472 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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58098
Re: surface area of cube  [#permalink]

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4
5
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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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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Hi,

Can you please elaborate this:

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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Joined: 02 Sep 2009
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Re: surface area of cube  [#permalink]

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rohu27 wrote:
Hi,

Can you please elaborate this:

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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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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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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Intern  Joined: 01 Mar 2014
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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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1
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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58098
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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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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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

Sent from my SM-G925I using GMAT Club Forum mobile app
Manager  B
Joined: 08 Sep 2016
Posts: 106
Re: If a 4 cm cube is cut into 1 cm cubes, then what is the  [#permalink]

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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.
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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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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.

Volume of a 4 cm cube = 4^3 = 64
Volume of a 1 cm cube = 1^3 = 1

Total number of 1 cm cubes which can be taken out of 4 cm cube after cutting = 64/1 = 64

Surface area of 4 cm cube = 6*4^2= 6*16

Surface are of 1 cm cube = 6*1^2 = 6
Surface area of 64 1 cm cube = 6*64

Total increase in surface area = 6*64 - 6*16 = 6*48
%ge increase in surface area = 6*48/6*16 x 100 = 300%

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