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The discussion focuses on optimizing the dimensions of a right circular cylinder oil can with a volume of 54π cubic inches to minimize material use. The minimum radius determined is 3 inches. The volume formula V = πr²h is used to express height in terms of radius, while the surface area A = 2πrh + 2πr² is derived for optimization. Participants confirm that the first derivative method is appropriate for finding the minimum surface area. The conversation concludes with agreement on the calculated dimensions.
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Got It, Thanks Guys
 
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Jack Jiang said:
An oil can is to be made in the form of a right circular cylinder to contain 54pi cubic inches. what dimensions of the can will require the least amt. of material.did anyone get the radius to equal 3?

Right on, the min is 3.
V=(Pi)R^2=54(Pi)
A=2(Pi)RH+2(Pi)R^2
Solve for H in volume, find minimum through first derivative.
 
Last edited:
V = \pi r^{2}h

Thus

A = 2\pi rh + 2\pi r^{2}
 

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