Jumphi97 wrote:

A product designer is trying to design the largest container possible hat will fit into a 6x12x14 box. Because of constraints in the manufacturing process, he must make the container in the shape of a cylinder, which will then be placed base down inside the box. What is the volume of the largest cylinder that can fit in the box?

A) 108π

B) 126π

C) 216π

D) 504π

E) 864π

Volume of a cylinder is \(\pi r^2 h\)

There is 3 configurations possible :

Height along side 6 --> Base on area of 12x14 --> Max radius is 6 : Vol = \(216 \pi\)

Hieght along side 12 --> Base on area of 6x14 --> Max radius is 3 : Vol = \(108 \pi\)

Height along side 14 --> Base on area of 6x12 --> Max radius is 3 : Vol = \(126 \pi\)

So max volume possible is (C) _________________

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1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

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