Tough Geometry please explain solution

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svd.kumar: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Tue Sep 21, 2010 7:38 am; Thanked: 4 times

by svd.kumar » Tue Jun 05, 2012 7:25 pm

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?

a) 200 pi
b) 160 pi
c) 360 pi
d) 192 pi

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Source: Beat The GMAT — Problem Solving | Tue Jun 05, 2012 7:25 pm

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

by Anurag@Gurome » Tue Jun 05, 2012 8:23 pm

svd.kumar 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?

If a right cylinder is fitted tightly inside a rectangular box, then the right cylinder will have the length equal to the length of one of the sides of the box and it will have a diameter equal to the length of the smallest of rest two sides of the box.

Volume of a right cylinder with height h and radius r is Ï€rÂ²h

Hence, possible combinations for the cylinder in this case

1. Height = 12, Diameter = 8 --> Radius = 4 --> Volume = 192Ï€
2. Height = 10, Diameter = 8 --> Radius = 4 --> Volume = 160Ï€
3. Height = 8, Diameter = 10 --> Radius = 5 --> Volume = 200Ï€ --> MAXIMUM

The correct answer is A.

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