Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register

A cylindrical canister in a rectangular box- volume

This topic has 2 expert replies and 4 member replies
pareekbharat86 Really wants to Beat The GMAT! Default Avatar
Joined
01 Nov 2012
Posted:
168 messages
Thanked:
1 times
A cylindrical canister in a rectangular box- volume Post Wed Nov 13, 2013 8:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

    OA is B

    My method:

    Volume of cylinder is Pi*r*r*h. So we need to know the combination of 2 of 6,8,&10 which will yield the maximum r*r*h.

    The following are the possible options-
    6/2 as radius and 8 inches height (3,3,8)- 72
    Similarly,
    3,3,10- 90
    8/2 as radius 4,4,6- 96
    OR 4,4,10- 160
    10/2 as radius 5,5,6- 150
    OR 5,5,8- 200

    Therefore i feel answer should be C

    _________________
    Thanks,
    Bharat.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 13, 2013 9:05 am
    pareekbharat86 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

    OA is B

    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 base 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 4

    Answer: B

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Wed Nov 13, 2013 9:11 am
    pareekbharat86 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

    OA is B

    My method:

    Volume of cylinder is Pi*r*r*h. So we need to know the combination of 2 of 6,8,&10 which will yield the maximum r*r*h.

    The following are the possible options-
    6/2 as radius and 8 inches height (3,3,8)- 72
    Similarly,
    3,3,10- 90
    8/2 as radius 4,4,6- 96
    OR 4,4,10- 160
    10/2 as radius 5,5,6- 150
    OR 5,5,8- 200

    Therefore i feel answer should be C
    To get a volume of 200(pi), you are saying that the height of the cylinder is 8 and the diameter is 10.
    This means that the cylinder's circular base is on the side with dimensions 6x10
    A circle placed on the side with dimensions 6x10 cannot have a diameter of 10 (it won't fit)

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Mathsbuddy GMAT Destroyer! Default Avatar
    Joined
    08 Nov 2013
    Posted:
    447 messages
    Followed by:
    1 members
    Thanked:
    25 times
    Post Wed Nov 13, 2013 9:17 am
    While your geometrical maths is good, there's a 'trick' to this question - which is hard to spot without a diagram:

    A) The biggest circle that will fit on a 10"x6" face has a radius of 3"
    B) The biggest circle that will fit on a 6"x8" face has a radius of 3" too
    C) The biggest circle that will fit on a 10"x8" face has a radius of 4"

    Therefore, the cylinders have volumes of:

    A) 3^2 * 8 * pi = 72pi
    B) 3^2 * 10 * pi = 90pi
    C) 4^2 * 6 * pi = 96pi

    Therefore the cylinder with radius 4 inches yields the largest volume!

    theCodeToGMAT GMAT Titan
    Joined
    14 Aug 2012
    Posted:
    1556 messages
    Followed by:
    34 members
    Thanked:
    448 times
    Target GMAT Score:
    750
    GMAT Score:
    650
    Post Wed Nov 13, 2013 9:37 am
    Another approach:

    Volume = pi * (r)^2 * h
    So, lets consider cases
    10x8 = (4)^2 * 6 = 96
    10x6 = (3)^2 * 8 = 72
    8x6 = (3)^2 * 10 = 90
    So, 10x8 is the dimension which results in maximum volume
    Attachments

    This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.


    _________________
    R A H U L



    Last edited by theCodeToGMAT on Sun Nov 17, 2013 9:22 am; edited 1 time in total

    Mathsbuddy GMAT Destroyer! Default Avatar
    Joined
    08 Nov 2013
    Posted:
    447 messages
    Followed by:
    1 members
    Thanked:
    25 times
    Post Sun Nov 17, 2013 9:10 am
    theCodeToGMAT wrote:
    Another approach:
    True that this gives you the biggest radius, but the question wants the biggest volume.
    It is only when each radius squared is multiplied by the corresponding length that we are convinced that this biggest radius option yields the biggest volume.

    theCodeToGMAT GMAT Titan
    Joined
    14 Aug 2012
    Posted:
    1556 messages
    Followed by:
    34 members
    Thanked:
    448 times
    Target GMAT Score:
    750
    GMAT Score:
    650
    Post Sun Nov 17, 2013 9:18 am
    Yep, actually I drew what you had explained in post above but I mistakenly skipped to include that calculation Wink

    _________________
    R A H U L

    Thanked by: Mathsbuddy

    Best Conversation Starters

    1 aditiniyer 26 topics
    2 Mo2men 13 topics
    3 rsarashi 11 topics
    4 neha shekhawat 9 topics
    5 Anaira Mitch 8 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    112 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    108 posts
    3 image description Matt@VeritasPrep

    Veritas Prep

    81 posts
    4 image description DavidG@VeritasPrep

    Veritas Prep

    79 posts
    5 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    73 posts
    See More Top Beat The GMAT Experts