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Tough Geometry please explain solution

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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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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 πr²h

Hence, possible combinations for the cylinder in this case
  • 1. Height = 12, Diameter = 8 --> Radius = 4 --> Volume = 192π
    2. Height = 10, Diameter = 8 --> Radius = 4 --> Volume = 160π
    3. Height = 8, Diameter = 10 --> Radius = 5 --> Volume = 200π --> MAXIMUM
The correct answer is A.
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