Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 28

The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
23 Feb 2012, 23:20
Question Stats:
57% (01:43) correct 43% (01:49) wrong based on 605 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59087

Re: The inside dimensions
[#permalink]
Show Tags
23 Feb 2012, 23:36
BANON 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 \(volume==\pi*{4^2}*6=96\pi\); So, the maximum volume is for \(r=4\). Answer: B. Hope it's clear. P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible.
_________________




Manager
Joined: 08 Dec 2012
Posts: 61
Location: United Kingdom
WE: Engineering (Consulting)

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
09 Mar 2013, 12:12
The three different sizes of faces of the rectangular box are: 6 x 8 8 x 10 6 x 10
Now in simple terms the question asks us to find the maximum radius of the cylinder which can be placed inside the box (reference to volume is an unwanted piece of information to solve this question)
The cylinder with the longest radius can logically sit only on the face of the box with the largest area which is 8 x 10.
This face of the box can accommodate a cylinder with diameter equal to the rectangular face's shortest length i.e 8. hence the maximum possible radius for the cylinder will be 4.
Hope the above is clear.




Intern
Joined: 22 May 2012
Posts: 2

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
16 Jun 2012, 07:37
So as a general rule, can we say that the longest side (10 in this case) can never be the Diameter of the circular base? I am having difficulty visualizing the reason of 10 not being a viable option for diameter.



Math Expert
Joined: 02 Sep 2009
Posts: 59087

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
16 Jun 2012, 07:48
planesmypassion wrote: So as a general rule, can we say that the longest side (10 in this case) can never be the Diameter of the circular base? I am having difficulty visualizing the reason of 10 not being a viable option for diameter. Ask yourself: on which face of the cube can you place a cylinder with the diameter of 10. Even if you consider the largest face (8*10), it's one dimension (8) will still be less than the diameter, so you cannot place the cylinder on it. Hope it's clear.
_________________



Intern
Joined: 22 May 2012
Posts: 2

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
16 Jun 2012, 08:11
Bunuel wrote: planesmypassion wrote: So as a general rule, can we say that the longest side (10 in this case) can never be the Diameter of the circular base? I am having difficulty visualizing the reason of 10 not being a viable option for diameter. Ask yourself: on which face of the cube can you place a cylinder with the diameter of 10. Even if you consider the largest face (8*10), it's one dimension (8) will still be less than the diameter, so you cannot place the cylinder on it. Hope it's clear. Drew a few figures and I think I understand now. When calculating , we can never take the larger side as diameter as the circular base would extend outside of the rectangular face. And in this case , only 3 cases possible where dia<height. Thanks bro!!



Manager
Joined: 23 Jan 2013
Posts: 128
Concentration: Technology, Other
GMAT Date: 01142015
WE: Information Technology (Computer Software)

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
07 Sep 2014, 05:53
Found this useful tip to be remembered as a thumb rule in another post .
As a rule of thumb, in such problems, select the second largest side as the diameter (note that it is the diameter and one has to calculate the radius by dividing by 2 before calculating the volume). And the left alone smallest side will be the height of the cylinder (as you need the two largest sides to enclose the bottom of the cylinder the only choice left out for height is the smallest side).



Intern
Joined: 29 Mar 2014
Posts: 14

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
12 Mar 2015, 08:57
Are there any similar questions to this for practice purposes? BANON 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



Math Expert
Joined: 02 Sep 2009
Posts: 59087

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
12 Mar 2015, 09:28
pinkcupcake wrote: Are there any similar questions to this for practice purposes? BANON 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 Similar questions to practice: theinsideofarectangularcartonis48centimeterslong138301.htmlarectangularboxhasdimensions12108incheswhatisthe28790.htmlaclosedcylindricaltankcontains36picubicfeetofwater134500.htmlwhatisthenumberofcansthatcanbepackedinacertain143776.htmlacylindricaltankofradiusrandheighthmustberedesign122366.htmlarectangularboxhasdimensions12108incheswhatisthe28790.html
_________________



Intern
Joined: 03 Jul 2015
Posts: 29

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
14 Oct 2015, 05:58
Bunuel wrote: BANON 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 \(volume==\pi*{4^2}*6=96\pi\); So, the maximum volume is for \(r=4\). Answer: B. Hope it's clear. P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible. what would be the problem if volume= pi* 4^2* 8 ??



Current Student
Joined: 21 Jul 2013
Posts: 105
WE: Securities Sales and Trading (Commercial Banking)

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
04 Dec 2015, 21:49
anik19890 wrote: Bunuel wrote: BANON 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 \(volume==\pi*{4^2}*6=96\pi\); So, the maximum volume is for \(r=4\). Answer: B. Hope it's clear. P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible. what would be the problem if volume= pi* 4^2* 8 ?? hi anik19890, volume= \(pi* 4^2* 8\) is not possible because if height = 8, we are only left with dimensions 10 & 6. Max of a cylinder's diameter from a base with dimensions 10 x 6 is 6, hence radius is \(6/2=3\). If the height used is 8, then max volume of the cylinder is \(pi*3^2*8\) = \(72pi\)



Director
Joined: 04 Jun 2016
Posts: 547

The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
17 Jul 2016, 03:54
BANON 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 For the base of the crate we have three values to choose from and we need to select any two ==> 3C2=\(\frac{3!}{2!*1!}\) = 3 ways in which it can be done. SO we will have three unique scenarios for the dimension of the base; the third value will become the height. 1st Case) Take base of 6 by 8; Radius 6/2=3 and the height 10 ; volume = 9*10 =90 2nd Case) Take base of 6 by 10; Radius 6/2=3 and the height 8; volume = 9*8= 72 3rd Case) Take base of 8 by 10, Radius 8/2=4 and the height 6; volume 16*6=96The volume is greatest when radius =4 Hence B is the answer
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8383
Location: United States (CA)

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
06 Mar 2017, 18:03
BANON 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 In order for the canister to stand upright in the box, the diameter of the canister must fit within the base of the box. Let’s test various scenarios to determine which will provide the largest volume of the canister. Remember, the volume of a cylinder = πr^2h. Keep in mind that the height of the cylindrical canister is the same as the height of the box. Scenario 1: The base of the box is 6 by 8 and the height is 10. Thus, the diameter of the cylinder = 6, which means the radius = 3. V = π(3)^2 x 10 = 90π Scenario 2: The base of the box is 6 by 10 and the height is 8. Thus, the diameter of the cylinder = 6, which means the radius = 3. V = π(3)^2 x 8 = 72π Scenario 3: The base of the box is 8 by 10 and the height is 6. Thus, the diameter of the cylinder = 8, which means the radius = 4. V = π(4)^2 x 6 = 96π Thus, the radius of the cylinder that provides the largest volume is 4. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4064
Location: Canada

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
19 Apr 2018, 14:57
BANON 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 of cylinder = pi(radius²)(height)There are 3 different ways to position the cylinder (with the base on a different side each time). You can place the flat BASE of the cylinder on the 6x8 side, on the 6x10 side, or on the 8x10 side If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6). So, the volume of this cylinder will be (pi)(3²)(10), which equals 90(pi)If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6). So, the volume of this cylinder will be (pi)(3²)(8), which equals 72(pi)If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8). So, the volume of this cylinder will be (pi)(4²)(6), which equals 96(pi)So, the greatest possible volume is 96(pi) and this occurs when the radius is 4Answer: B Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Intern
Joined: 01 Jul 2018
Posts: 7

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in
[#permalink]
Show Tags
28 Oct 2018, 07:08
volume of Cuboid = 480 To get placed inside the cuboid Volume of cuboid= volume of cylinder pi r^2 h = 480
Concept of solving the unknown To stand upright, the cylinder canister should have a height equal to the cuboid largest side (i.e= 10)
solving for above eq. r~4
(All dimensions are in inches and volume inches^3)



Intern
Joined: 26 Mar 2019
Posts: 35

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
04 Apr 2019, 01:04
I understand that the diameter h=10,(r=5) cylinder cannot be put in the rectangular box.
6 can be put(r=3)
But how come diameter 8 (r=4) can be fit into the cylinder.because that is not going to fit into the mouth of rectangular box, in my visualization i can fit only r=3 ( d=6)....
just think about a circle in square.. the circle in square it touches all sides thats why diameter is equal to all 4 sides.
But when it comes for rectangular side the diameter is not equal to all 4 sides. The mouth of the box is narrow in rectangular because of lenght and width. So how come you can put 2 diameter(8,6) and it touches the all sides in the rectangular box just like square mouth???
Need help not getting this thing in my head
Posted from my mobile device



Intern
Joined: 26 Mar 2019
Posts: 35

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
04 Apr 2019, 01:07
Bunuel wrote: BANON 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 \(volume==\pi*{4^2}*6=96\pi\); So, the maximum volume is for \(r=4\). Answer: B. Hope it's clear. P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible. I understand that the diameter h=10,(r=5) cylinder cannot be put in the rectangular box. 6 can be put(r=3) But how come diameter 8 (r=4) can be fit into the cylinder.because that is not going to fit into the mouth of rectangular box, in my visualization i can fit only r=3 ( d=6).... just think about a circle in square.. the circle in square it touches all sides thats why diameter is equal to all 4 sides. But when it comes for rectangular side the diameter is not equal to all 4 sides. The mouth of the box is narrow in rectangular because of lenght and width. So how come you can put 2 diameter(8,6) and it touches the all sides in the rectangular box just like square mouth??? Need help not getting this thing in my head Posted from my mobile device



Manager
Joined: 02 Jan 2017
Posts: 58
Location: India

Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
Show Tags
11 May 2019, 00:15
GMATPrepNow wrote: BANON 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 of cylinder = pi(radius²)(height)There are 3 different ways to position the cylinder (with the base on a different side each time). You can place the flat BASE of the cylinder on the 6x8 side, on the 6x10 side, or on the 8x10 side If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6). So, the volume of this cylinder will be (pi)(3²)(10), which equals 90(pi)If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6). So, the volume of this cylinder will be (pi)(3²)(8), which equals 72(pi)If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8). So, the volume of this cylinder will be (pi)(4²)(6), which equals 96(pi)So, the greatest possible volume is 96(pi) and this occurs when the radius is 4Answer: B Cheers, Brent Hi Brent, I am not able to visualise this. how can we take each face say 6*8 and decide which will be the diameter




Re: The inside dimensions of a rectangular wooden box are 6
[#permalink]
11 May 2019, 00:15






