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anonymous
 5 years ago
An open metal tank with a square base is made from 12m^2 of sheet metal. Find the length of the side of the base for the volume of the tank to be a maximum and find this maximum volume
anonymous
 5 years ago
An open metal tank with a square base is made from 12m^2 of sheet metal. Find the length of the side of the base for the volume of the tank to be a maximum and find this maximum volume

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think you should use inequalities, and finaly draw a graph using them. Right sstarica?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm, it's more like an optimization problem where you have to find the Absolute maximum in this case.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0he base is a square, but the other parts take shape of a cylinder, weird ._.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't figure out a sketch for this one >_<, with no sketch, no formula, no answer sorry

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maxima problem.. determine what subject to be maximize or minimize; in this case, the volume of a tank.. V = lwh and in this case the l is equal to the w. therefore V = w^2*h then, give the constraint of the problem.. in this case; the material to be use.. only 12 m^2 Make an equation for the constraint: that is, the formula for the surface area..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you mean L not I right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, now we have the general function which is: V = w^2h

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the constraint: the surface area of a tank, cube with open on the top, which means there are 5 faces only. one on the bottom, and four on the sides. The surface area on the bottom is w^2 and the surface area on the side is wh. since there are 4 side faces, 4w^2 therefore the total surface area is: w^2 + 4wh = 12 m^2(meter squared)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0from the general function stated by sstarica, express h in terms of w from my total surface area equation, then we will have a function of V in terms of w..

radar
 5 years ago
Best ResponseYou've already chosen the best response.0The problem states only the base is made from material that is 12 sq material.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Never mind it does probably include the sides in the that 12 sq meters of material. Come on fellows go ahead and work this out. I can't envision construction of this tank without some waste in the material (cutting out the corners). I guess they could just press it into a mold!!!

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Can we safely assume that the base is a square? i.e. length = width.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as what i understand the problem. the tank is square base, and the tank is made from 12m^2. The problem does not define how the tank is constructed.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0do we assume that the sheet metal is a square to begin with? or simply 12m^2 of rectangular shape?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0most of these problems have you cut corners and fold the sides..... but that is an assumption for this one....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for me, the assumption is that the total surface area is 12 m^2. :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Cant we just buy a tank thats already large enough to use? :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol., then you are the consumer, not the designer.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I say we go to the ag store and buy the tank.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0If we assume only the base is 12 sq meters then we have no limit on the height of the sides that means you could have a mighty big tank!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, that is why it must be assumed that the total surface area of the tank is 12 m^2. I think I already give the equation for that.. using that assumption we can have a solution.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0whats the measurements of the sheet metal tho? is it: 1,12 2,6 3,4 or some decimalized monstrosity?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0like 4sqrt(3), 4sqrt(3) ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0uhh..that shoulda been 2sqrt(3) s but you know....the keyboard hates me :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0also, it just says tha the base is square; it doesnt say that the tank itself is square.... hmmmm

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I tried to solved it. the answer is: width = 2m length = 2 m (for square base) height = 1 m therefore the total volume is 4 m^3, the total surface area is 12 m^2. ^_^

radar
 5 years ago
Best ResponseYou've already chosen the best response.0That works out for the amount of material.....but is it the maximum volume, I'm thinking it is but can't prove it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0try use the equation: V = w^2 * h (square base) Surface area = 12 m^2 = w^2 (square base) + 4 * w * h (four faces of the sides of the tank) solve for h in terms of w: h = (12  w^2) / 4w therefore, the volume becomes V = (w^2) * (12w^2)/4w or V = (12w  w^3)/4 then derive V with respect to w

radar
 5 years ago
Best ResponseYou've already chosen the best response.0That would be w=2 I guess that is the proof that is needed. Thanks for the step by step procedure.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[V=(12ww ^{3})/4=3ww ^{3}/4=3w1w ^{3}/4\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow., how did you do that radar?

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Set to 0 \[33w ^{2}/4=0\] \[3w ^{2}/4=3\] Multiplying both sides by 4/3 \[w ^{2}=4\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Hey, Janjor did the ground work! lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah! i think i don't understand what you mean by "ground" lol

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Set up the foundation (foundations are usually on the ground)
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