Question

Asked Oct 20, 2019

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A crate open at the top has vertical sides, a square bottom, and a volume of 256 cubic meters. Using the labels shown in the figure, write the surface area S as a function of x.

S(x) =

If the crate has the least possible surface area, find its dimensions.

x = meters

y = meters

z = meters

S"(x) = (value for your solution for x)

Step 1

Given,

A crate open at the top has vertical sides, a square bottom, and a volume of 256 cubic meters.

Let the length of the side of the bottom square be x m then

Let breadth of the bottom square be y m.

So, x = y

Let height of the cube be z in meters

Step 2

Now,

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