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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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?

Re: A 4 cm cube is cut into 1 cm cubes. [#permalink]

Show Tags

25 Sep 2008, 13:44

1

This post received KUDOS

4 cm cube has 6 facets of 16 sq. cm each (96 sq. cm in all). After cutting the cube into 1 cm cubes we'll end up with 64 1 cm cubes. Each will have the surface area of 6 sq. cm. \(\frac{6*64}{6*16} = \frac{4}{1} = 400%\). Therefore the increase in surface area must have been 300%. Did that without looking into the OE . Let's check now...
_________________

m01-Q11.....explanation not clear...help please [#permalink]

Show Tags

02 Oct 2008, 11:53

A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

4% 166% 266% 300% 400% The easiest way to solve this problem is to calculate the original surface area and then the final. The original area is 4*4*6. The new area is 1*1*6*4*4*4. So, the difference is 1:4. Therefore, the increase is 300%. You can also solve it logically, but that's more risky.

The correct answer is D.

I couldnt quite understand the explanation here...

The original area is 4*4*6 i agree, but the new area should be 1*1*6*4, why has 4 been multiplied 3 times. Could someone please explain. The question says that the original cube has been cut into 1cm cubes so there are 4 cubes in all now, and every cube will have 1cm side so the SA of every cube will be 1*1*6 and since we have four such cubes the Area of all these will be 6*4.

Re: m01-Q11.....explanation not clear...help please [#permalink]

Show Tags

03 Oct 2008, 09:10

4

This post received KUDOS

Hi Siddarth,

You have a 4 cm cube, so the surface area is 4*4(area of one side)*6 sides..= 96, which you agree with. Then figure out how many 1 cm cubes can fit into 4 cm cube. 4 cm cube's Volume is 4*4*4 = 64. A 1 cm cube's Volume is 1*1*1 = 1 so 64/1 = 64 little cubes.

Now for the surface area of each little cube: 1*1(area of one side of one cube) * 6 sides= 6 surface area of one cube. So, 64 cubes * 6 surface area/cube = 384 Total surface area.

So, 384 new/96 old is 4 times or 400% so 300% difference or 288 (difference in area)/96 (original) = 3 or 300% difference.

total 4*4*4 = 64 squares with side 1cm total surface area = 64 * 6 cm square surface area for 4cm cube is = 16 * 6 cm square

so surface area increase = (64-16)/16 * 100 = 300%

how did you know that there were going to be 64 additional squares?

it is 300% - I like how one of the participants just used l and did not input a variable in. one knows that there are 64 additional squares because discussed 3-dim shapes are cubes therefore all sides are equal. Consequently one can fit (4)/(1) lengths into one dimension = 4. So 4 little cubes in on dimension and then cube it.

Hmmm that was a bit complicated - hope that made sense.

surface area of 4 m cube = 6*4*4 surface area of 1 m cube = 6 no of cubes = 4*4*4 increase in surface area = (4*4*4*6 - 6*4*4)*100/6*4*4 = 300% hence D
_________________

Surface area of 4 cm cube = (surface area of one side)*(number of sides) = (4*4) * (6) Surface area of all cubes: = (number of cubes)*(surface area of cube) = (4*4*4) * (6)

By simply looking at these two equations we see that there is 4 times more surface area with the little cubes, thus 300% increase.

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 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.

Answer: D.

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

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