GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 31 May 2020, 03:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a cube with the length of the side of 4 cm is cut into smaller cube

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 28 Aug 2010
Posts: 139
If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 15 Jan 2011, 14:07
3
40
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:55) correct 36% (02:15) wrong based on 547 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 15 Jan 2011, 14:34
5
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.


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
_________________
General Discussion
Intern
Intern
avatar
Joined: 15 Jan 2011
Posts: 36
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 15 Jan 2011, 21:04
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.

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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 16 Jan 2011, 01:55
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.

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.


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).
_________________
Intern
Intern
avatar
Joined: 25 Apr 2013
Posts: 5
Location: India
Concentration: Strategy, Marketing
Schools: INSEAD Jan '15
GPA: 2.7
WE: Information Technology (Computer Software)
Re: M01 #11  [#permalink]

Show Tags

New post 03 May 2013, 08:53
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)
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1708
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 04 Mar 2014, 03:09
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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 04 Mar 2014, 03:15
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.

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.


Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
_________________
Intern
Intern
avatar
Joined: 01 Mar 2014
Posts: 5
GMAT Date: 05-23-2014
GMAT ToolKit User
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 13 Aug 2014, 03:08
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
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 13 Aug 2014, 05:40
Manager
Manager
avatar
B
Joined: 21 Jun 2011
Posts: 55
Location: United States
Concentration: Accounting, Finance
WE: Accounting (Accounting)
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 23 Nov 2014, 11:58
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.

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 24 Nov 2014, 05:37
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.

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


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.
_________________
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 205
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 03 Nov 2018, 23:21
1
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%
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 717
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 24 Apr 2019, 09:17
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%

Answer D
Manager
Manager
avatar
G
Joined: 30 May 2019
Posts: 82
CAT Tests
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 12 May 2020, 07:17
1
https://gmatclub.com/forum/if-a-cube-wi ... 80681.html
although phrased little differently, still absolutely the same question, Bunuel
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

Show Tags

New post 12 May 2020, 07:28
GMAT Club Bot
Re: If a cube with the length of the side of 4 cm is cut into smaller cube   [#permalink] 12 May 2020, 07:28

If a cube with the length of the side of 4 cm is cut into smaller cube

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne