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 350,000 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:

The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
17 Mar 2010, 17:30

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

53% (02:01) correct
48% (01:24) wrong based on 92 sessions

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
17 Mar 2010, 19:02

hb05sv wrote:

Can someone show me how to solve the following question?

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume? A)3 B)4 c)5 D)6 E)8

Correct Ans is B.

let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area. so B - 4

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
17 Mar 2010, 19:26

kp1811 wrote:

let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area. so B - 4

Nice explanation -

To be more specific, logically, for any face down of the cube, the smaller length only can be the diameter of the cylindrical canister. So either ways, it is 6 or 8. The height will be either the shortest or the longest dimension accordingly.

Volume of cylinder is Pi * r squared * h. The greater the value of r^2*h, the greater the volume. _________________

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
18 Mar 2010, 16:04

hb05sv wrote:

BarneyStinson, Can you explain why logically the diameter of the cylinder will be one of the shortest?

Because if the diameter were wider say 8", it won't fit into a box that has one side 6", when the face down is 8" X 6". You should definitely read my blog!!! _________________

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
20 Aug 2010, 06:22

1

This post received KUDOS

kp1811 wrote:

hb05sv wrote:

Can someone show me how to solve the following question?

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume? A)3 B)4 c)5 D)6 E)8

Correct Ans is B.

let the face on which the cylinder is placed is 6 by 8. In this case the volume will be pi* 3^2*10 = 90pi (here r =3inches)

If the cylinder is placed on the face having dimensions 8 by 10 then volume in that case will be pi* 4^2* 6 = 96pi (here r = 4inches)

If the cylinder is placed on the face having dimensions 6 by 10 then volume in that case will be pi* 3^2* 8 = 72pi (here r = 3inches)

so for r = 4inches the cylinder will have maximum area. so B - 4

Sorry guyz but dont understand your ways

My approach is;

pi approx. = 3,14

The box volume is 480 so;

Cylinder max. volume should be pi*5^2*8 = 200pi means more then 600 so cant be, If the radius cant be 5 so it should be 4;

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
21 Aug 2010, 15:17

1

This post received KUDOS

Since we want Max Volume for cylinder hence Max Vol can only max if the Radius is maximum

We can always have Cylinder with radius 3 in this Box but we need max radius if we take (6 and 8) or (6 and 10) or (10 and 8)

So let us pick 5 as radius so the diameter will be 10 but other two sides are 8 and 6 which cause a cylinder with 10 radius out of the box. Hence 5 is not the answer Anything above 5 i.e 6 and 8 are gone Now we come to our last option 4 if we take sides 10 and 8 as the base we can surely incorporate cylinder inside the box hence our answer is B i.e. 4.

Try to give it a thought because I have not used any calculation to solve this question. And don't forget in Gmat Exam we need to conserve all our energies because after Quants exam the beast awaits......VERBAL!!!!!! _________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed." - Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
23 Nov 2011, 08:40

The above mentioned solutions are correct, but from my perspective the question could be misleading (at least for non-natives). The question states "a cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on (ANY) one of its six faces". Since the canister has a fixed volume and we cannot be sure on which face the wooden box will stand, we would have to assume that it could also stay on the smallest possible area, namely 6 by 8. If so, the correct solution, 4, would be wrong, since the diameter would exceed the side length 6. Sorry if I confused you guys, but I personally dislike such questions, since they inhabit the potential for incorrect choices only due to the unclear phrasing of the question.

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
14 Apr 2015, 16:44

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
15 Apr 2015, 02:48

Expert's post

hb05sv wrote:

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

\(volume_{cylinder}=\pi{r^2}h\)

If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*10=90\pi\); If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*8=72\pi\); If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*6=96\pi\);

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]
15 Apr 2015, 02:48

Expert's post

Bunuel wrote:

hb05sv wrote:

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

\(volume_{cylinder}=\pi{r^2}h\)

If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*10=90\pi\); If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*8=72\pi\); If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*6=96\pi\);

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...