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?
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 \piSo max volume possible is (C)
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry
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