PLS HELP ME WITH THIS!! I had covid when this was taught to us so I had to stay in a hospital. This is an example problem.

[MARCELA]

"A closed rectangular box that would enclose 36 cubic centimeters is to have a base whose
length is twice its width. What should the dimensions of the box be so that the material to be used in
its construction is least?'

Can anyone help me answer this? Showing solutions will be a great help!! <3

 

[Deleted member 4993]

"A closed rectangular box that would enclose 36 cubic centimeters is to have a base whose
length is twice its width. What should the dimensions of the box be so that the material to be used in
its construction is least?'

Can anyone help me answer this? Showing solutions will be a great help!! <3

If this is "truly" example problem - you should have the solution in the book!! Did you look for it?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Steven G]

Can you at least write the equation for the volume of the box? Surely you know how to compute the volume of a box?

 

[P.K.Tandon]

If width = x cm, Length of the base = 2 x, and let height = h cm.

Volume (V) = x*2x*h = 2 x²h, Surface area = 4 x² + 6 x h
Substitute value of volume and find x in terms of h
Substitute this value of x in equation of Surface area
Surface area (S) = terms involving h and constants.
Next Step : find ds/dh ...........
Now proceed to find the h for the minimum value of Surface Area ( i.e. material)

 

[lookagain]

If width = x cm, Length of the base = 2 x, and let height = h cm.

Volume (V) = x*2x*h = 2 x²h, Surface area = 4 x² + 6 x h
Substitute value of volume and find x in terms of h
Substitute this value of x in equation of Surface area
Surface area (S) = terms involving h and constants.
Next Step : find ds/dh ...........
Now proceed to find the h for the minimum value of Surface Area ( i.e. material)

P.K. Tendon, you are missing "cm" for the base. All of your coefficients and
variables need to right up against each other for a product. For example,
"6 x h" looks closer to "6 ex h," or even "6 multiplied by h." You should give
the formula volume and then substitute the quantities in the correct order.
Likewise, you should do that for the surface area so the student can tell
where it comes from.

Here is a redo of some pertinent parts:

Let the dimension of the width = x cm. Then the dimension of the
base (length) = 2x cm, and the dimension of the height = h cm.

Volume (V) = (length)(width)(height) = \(\displaystyle \ (2x)(x)(h) \ = \ 2x^2h\)

Surface area (S) = \(\displaystyle \ 2(2x^2) \ + \ 2(2xh) \ + \ 2(xh) \ = \ 4x^2 + 6xh\)