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

OA: CCase 1: Base Dimensions \(=6*12\); Height \(= 14\)

then radius of cylinder will be \(\frac{6}{2}=3\) and height will be \(14\)

Volume \(= \pi r^2h =\pi *3^2*14=126\pi\)

Case 2: Base Dimensions \(=6*14\); Height \(= 12\)

then radius of cylinder will be \(\frac{6}{2}=3\) and height will be \(12\)

Volume \(= \pi r^2h =\pi *3^2*12=108\pi\)

Case 3: Base Dimensions \(=14*12\); Height \(= 6\)

then radius of cylinder will be \(\frac{12}{2}=6\) and height will be \(6\)

Volume \(= \pi r^2h = \pi *6^2*6=216\pi\)

(Largest Cyclinder)
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