Geometry problem

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pm; Thanked: 4 times; Followed by:1 members

Geometry problem

by Troika » Thu May 17, 2012 7:36 am

A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

OA: 200pie

Source: Manhattan GMAT Geometry 4th edition, pg. 49.

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 am; Thanked: 56 times; Followed by:7 members; GMAT Score:690

by LalaB » Thu May 17, 2012 9:51 am

the largest volume is possible, if the height is 8, and the rest (10 and 12) are the legs.

so, the volume =5^2*8=25*8=200

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Thrills4ever: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu May 12, 2011 12:47 pm; Thanked: 1 times

by Thrills4ever » Thu May 17, 2012 6:34 pm

I think it should be 200pi since V = pi*r^2*h

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Thu May 17, 2012 8:00 pm

HG10 wrote:A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

OA: 200pie

Source: Manhattan GMAT Geometry 4th edition, pg. 49.

Volume of cylinder = pi * rÂ² * h.
For maximum volume, radius should be maximum because it has a square power.
This is possible if we take the base of cylinder as the base of the box which is 12*10.
Then the diameter is 10 for the cylinder, as it has to be lesser of 10 and 12.
Or radius is 10/2 = 5 and height is 8.
So volume is pi * 5Â² * 8 = 200pi.

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pm; Thanked: 4 times; Followed by:1 members

by Troika » Sat May 19, 2012 9:55 pm

Guys, thank you for your responses.

I just have one question, i.e. if radius should me maximum for maximum volume, why select r=10/2, why not r=12/2 and h=10 instead of h=8?

The only battle you can loose, is the one you abandon.

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 am; Thanked: 56 times; Followed by:7 members; GMAT Score:690

by LalaB » Sat May 19, 2012 11:42 pm

HG10 wrote:Guys, thank you for your responses.

I just have one question, i.e. if radius should me maximum for maximum volume, why select r=10/2, why not r=12/2 and h=10 instead of h=8?

u better try to draw ur desired figure. if u do so, u will find out that it is impossible to have two sides 10 and 12, and get 12/2,since the max value of ur side is 10.

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)