A box with a square base and no top must have a volume of 10000cm^3. Determine the dimensions of the box that minimize the amount of materials used. The smallest dimension possible is 5cm
What is the restriction in here? I already found the answer h = 13.6 and w=l = 27.1
but dont know what is the restrictions
Stacey Warren - Expert brainly.com
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restriction is \(w^2h=3000\)
where is that 3000 from??
first I thought is 100 because 100x1000 gives 10000 (so cant have any volume)
but when i plug it into the surface area equation, it gives a huge number..
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oh because i wasn't paying attention doh
should have been \(w^2h=1000\)
can u tell me how to get it...kinda confuse
you are given that the volume is fixed, that is it must be 1000 square whatever
and the base is a square with area \(w^2\) assuming you are using "w" as the variable representing the lenght of the base, and the height is "h" if you use that variable for height
volume is therefore \(w^2h\) area of the base times the height.
The very first problem on this page is almost identical to your original problem. :)
The equation I have is
S = x^2 + 40000/x
(when i combine the 2 equations together)
so if i plug in x = 1000 , then i get 1000040 for surface area
so doesnt seem restricted?
oh really, i will take a look at it! thks mathteacher
so you have two representations for the volume, one in terms of variables \(w^2h\) and the other a number you know, namely 10000, giving
isnt it w^2h = 10000
@mathteacher1729 but that question only shows the min value, but not the restrictions