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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## rectangular wooden box tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 2 member replies ## rectangular wooden box 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 this question Area could be max when radius = 5 and height = 8 A= 3.14 *25*8 = 100 * 3.14 Is it ? Then answer should be C but OA is B. _________________ Thanks & Regards vishalwin ------------------------------------ GMAT Score - 530 I will BEAT the GMAT! Legendary Member Joined 03 Feb 2014 Posted: 2063 messages Followed by: 133 members Upvotes: 955 GMAT Score: 800 If the radius were 5, the cylinder would not fit inside the box. The biggest face of the box is 8 x 10. A circle with a radius of 5 has a diameter of 10, or is 10 wide, in all directions. So, a cylinder with a radius 5 would therefore not fit in a box unless at least one face of that box were to have dimensions of at least 10 x 10. Given that you are constrained by either width 8, on the 8 x 10 end, or width 6, on the 6 x 8 or the 6 x 10 end, the greatest two diameters possible are 8 and 6, and the greatest two radii possible are 8/2 = 4 and 6/2 = 3. Formula for the volume of a cylinder: Ï€ x rÂ² x Height Radius 3 on the 6 x 10 end generates Ï€ x 3Â² x 8 = 72Ï€ (You don't really need to calculate this one as the next one will have the same radius and a greater height, and so the next will will obviously have a greater volume.) Radius 3 on the 6 x 8 end generates Ï€ x 3Â² x 10 = 90Ï€ Radius 4 on the 8 x 10 end generates Ï€ x 4Â² x 6 = 96Ï€ So the correct answer is B. _________________ Marty Murray GMAT Coach m.w.murray@hotmail.com https://infinitemindprep.com/ In Person in the New York Area and Online Worldwide Last edited by Marty Murray on Wed Nov 25, 2015 7:52 am; edited 2 times in total ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12422 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 vishalwin 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(radius^2)(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)(3^2)(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)(3^2)(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)(4^2)(6), which equals 96(pi) So, the greatest possible volume is 96(pi) and this occurs when the radius is 4 Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9942 messages Followed by: 492 members Upvotes: 2867 GMAT Score: 800 Hi vishalwin, You have to be careful with how you set-up this question (drawing pictures would likely help though). Since none of the sides of the box is a square, the diameter of the cylinder is limited by the SHORTER dimension of the side that is face down. For example, if the 6x8 side was face down, then the cylinder would have a maximum diameter of 6. That limitation holds true with the other two options as well (6x10 face down ---> max diameter = 6; 8x10 face down --> max diameter = 8). Keeping that in mind, what answer would you get if you solved as normal? GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Master | Next Rank: 500 Posts Joined 13 Nov 2015 Posted: 137 messages Followed by: 2 members Upvotes: 1 Vishalwin, the cylinder could be placed on one of three sides: 6x8 , 6x10 , 8x10 however you need to notice that the diameter of the cylinder will be constrained by the smaller side for example if it is placed on the side 6x8, the diameter can't be 8, because the other dimension of the box is 6, so the cylinder won't fit in; hence, we are constrained by the smaller side in every case of the three cases. so lets consider case 1: 6x8 maximum diameter here will be 6 so radius is 3, and height is the other dimension of the box which is 10 so the volume will be 9pix10 = 90 pi case 2: 6x10 we are constrained by the smaller dimension, 6, which will be the maximum diameter for the cylinder. radius will still be 3, so volume will be 9pi x 8 = 72pi --> here 8 is the third dimension of the box case 3: 8x10 the maximum diameter can be 8, so radius will be 4 volume equal: 16pi x 6 = 92pi i hope you got it cheers vishalwin 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 this question Area could be max when radius = 5 and height = 8 A= 3.14 *25*8 = 100 * 3.14 Is it ? Then answer should be C but OA is B. ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2636 messages Followed by: 114 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 The idea is right, but try drawing a circle with diameter 10 inside an 8x10 rectangle and you'll see what goes wrong. I run into this issue myself sometimes, and drawing a figure to scale usually clears things up. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? 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