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605-655 Level|   Geometry|      
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ajit257
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If a cube with the length of the side of 4 cm is cut into smaller cube 15 Jan 2011, 15:07
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If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

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


M01-11

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D
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Bunuel
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If a cube with the length of the side of 4 cm is cut into smaller cube 15 Jan 2011, 15:34
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ajit257
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.
Show more

A cube has 6 faces.

The surface area of a cube with the length of the side of 4 cm is \(6*4^2=6*16\) \(cm^2\).

Now, since the volume of the big cube is \(4^3=64\) \(cm^3\) and the volume of the smaller cubes is \(1^3=1\) \(cm^3\), then when the big cube is cut into the smaller cubes we'll get \(\frac{64}{1}=64\) little cubes. Each of those little cubes will have the surface area equal to \(6*1^2=6\) \(cm^2\), so total surface are of those 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): \(\text{Percent} = \frac{\text{Change}}{\text{Original}}*100\)

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


Answer: D
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rohu27
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If a cube with the length of the side of 4 cm is cut into smaller cube 15 Jan 2011, 22:04
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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
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.

Answer: D.

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

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

Answer: D.
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If a cube with the length of the side of 4 cm is cut into smaller cube 16 Jan 2011, 02:55
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rohu27
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
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.

Answer: D.

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

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

Answer: D.
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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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If a cube with the length of the side of 4 cm is cut into smaller cube 03 May 2013, 09:53
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Total Surface Area of bigger cube = 6a^2 = 6*(4)^2 = 96
Total Surface Area of 1 smaller cube = 6*a^2 = 6*(1)^2 = 6

Let 'x' be total number of small cubes formed after cutting
Volume of bigger cube = (x) Volume of smaller cube => 4^3 = (x)1^3 => x = 64
Hence,total surface area of 64 smaller cubes = 64 * 6 = 384

Now % increase in Total Surface Area = [(Final Area - Initial Area)/Initial Area]*100=> [(384-96/96 )]*100 = 300%
Hence Ans (D)
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If a cube with the length of the side of 4 cm is cut into smaller cube 04 Mar 2014, 04:09
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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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If a cube with the length of the side of 4 cm is cut into smaller cube 04 Mar 2014, 04:15
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ajit257
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.

Answer: D.

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

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

Answer: D.
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If a cube with the length of the side of 4 cm is cut into smaller cube 13 Aug 2014, 04:08
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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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Bunuel
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If a cube with the length of the side of 4 cm is cut into smaller cube 13 Aug 2014, 06:40
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amirsalehi
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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The area cannot be in units, it's in square units, so 4cm can only mean length of something.
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If a cube with the length of the side of 4 cm is cut into smaller cube 23 Nov 2014, 12:58
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ajit257
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.

Answer: D.

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

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

Answer: D.
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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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If a cube with the length of the side of 4 cm is cut into smaller cube 24 Nov 2014, 06:37
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Bunuel
ajit257
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.

Answer: D.

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

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

Answer: D.

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
Show more

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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If a cube with the length of the side of 4 cm is cut into smaller cube 04 Nov 2018, 00:21
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Surface area of larger cube = 6 * 4*4 = 96
No of cubes of 1cm each = 4*4*4 = 64
surface area of 64 small cubes = 64 * 6 * 1*1 = 384

% Inc = (384-96) 100 / 96
= 300%
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If a cube with the length of the side of 4 cm is cut into smaller cube 24 Apr 2019, 10:17
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ajit257
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.
Show more

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%

Answer D
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If a cube with the length of the side of 4 cm is cut into smaller cube 04 May 2022, 13:48
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The volume of the cube is 64 and its surface area is 6*16 = 96. We can carve out 64 cubes of 1x1 out of the bigger/original cube. The surface are of the little cubes are 6(1x1) = 6. We got 64 of them --> 64*6. (64*6- 96)/96 * 10* = 300.
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If a cube with the length of the side of 4 cm is cut into smaller cube 30 May 2024, 09:14
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