If 48 square meters of sheet metal are to be used in the construction of an open tank with a square base; find

Question

mathematics-integrals

Answer 1

The end of your question got cut off, but I'm going to assume you want to maximize the volume.

Let x be the length of one side of the base, and h be the height. Then the area of the base is x², and the area of each side is xh.

SA = x² + 4xh = 48

Solve for h: h = (48 - x²)/4x

The volume is x²h. Substituting the value above:

V(x) = x²(48 - x²)/4x = 12x - 1/4x³

Differentiate and set equal to 0:

V'(x) = 12 - 3/4x² = 0

48 - 3x² = 0
48 = 3x²
16 = x²
4 = x

So h = (48 - (4)²)/4(4) = 32/16 = 2

So the dimensions that maximize the volume are a side length of 4 and a height of 2.

Answer 2

The question perhaps should be what's the optimum volume of a square base tank that you can obatin by by using 48 sq. m.

otherwise you can have many square base sizes and tank heights to use up the given sheet metal. You have not set any constraints or criterias of tank construction.

Do you want the height = the side of the sq. base. That is one option.

Answer 3

The surface area s= xx+4xy =48, where x is the size of square bottom, y is height of tank; thence y=(48/x –x)/4 and v= xxy = xx*(48/x -x)/4 is volume of tank, being max when dv/dx = 0 or v’ = 12 –0.75xx =0, hence x = 4 m, y =2 m, v = 32 m^3;

Answer 4

At best the problem needs to be re-defined. But I will answer.

This is a maxi-ma problem. In calculus. Assuming that you want the tank to hold maximum volume of water, for the amount of material at hand.

let say base is axa, and height is h so V=axaxh, 'h' may or may not be equal to 'a'.

We also know that neglecting the material for joint,

48=(axa) + 4(axh), 'h' may or may not be equal to 'a'.

Say if we know that for a given surface area cub is the biggest volume then, 'a'cube =V

48=5 ('a' square).
48/5=('a' square).=9.6

a=3.1meters each side
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Above is the easiest solution.
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This means if Volume is V(max)=
In case the statement is falls and Say if we do not know for sure that for a given surface area cub is the biggest volume, then 'a' is not equal to 'h'.

V(max)=axaxh

Answer 5

If the question is: find the dimesion that would hold the largest volume... then the answer is... 3.09838667697 meters along each side.

Answer 6

find what ?
the money for the metal ?

Answer 7

you havent completed the whole problem dude!

Answer 8

wrong question

Answer 9

please re-send you question correctly worded.