An Open Rectangular Box Having a Volume of Is

question 179

Essay

An open rectangular box having a volume of is to be constructed from a tin sheet.Find the dimensions of such a box if the amount of material used in its construction is to be minimal.
Hint: Let the dimensions of the box be x by y by z.Then, xyz = 108 and the amount of material used is given by S = xy + 2yz + 2xz.Show that Minimize f(x, y)
x = __________
y = __________
z = __________

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Definitions:

Orthopedist

A specialist who diagnoses and treats diseases and disorders of the muscles and bones.

Optical System

A combination of lenses, mirrors, and other devices that manipulate light to produce a desired image or effect.

Joint

The point at which two or more bones meet in the body, allowing for movement and flexibility.

Body Cavity

A hollow or space within the body that contains and protects internal organs, such as the chest or abdominal cavities.