anonymous
  • anonymous
2700 of material is avaiblr to make a boc with a square base and a open top. determine the largesst volume of the box
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
the open top thing is confusing me
anonymous
  • anonymous
i am only missing 2700 cm2

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ganeshie8
  • ganeshie8
|dw:1433741377518:dw|
ganeshie8
  • ganeshie8
surface area of box = (surface area of base) + (surface area of sides) = x^2 + 4xh we're given surface area equals 2700, so \[x^2+4xh=2700\tag{1}\]
ganeshie8
  • ganeshie8
next, see if you can write an expression for the volume of box
anonymous
  • anonymous
o yea i think the SA formula was confusing me how do u get it
anonymous
  • anonymous
@ganeshie8 is the vloume=lwh
ganeshie8
  • ganeshie8
for surface area, you just add up the areas of all the sides
ganeshie8
  • ganeshie8
how many sides does that box have ?
anonymous
  • anonymous
um 6
ganeshie8
  • ganeshie8
careful, it has no top
ganeshie8
  • ganeshie8
there is one base, which is a square and four lateral sides
ganeshie8
  • ganeshie8
so in total it has 5 faces
ganeshie8
  • ganeshie8
whats the area of base ?
anonymous
  • anonymous
x2?
ganeshie8
  • ganeshie8
Yes, area of base = \(x^2\)
ganeshie8
  • ganeshie8
next notice that each lateral face has same dimensions : width = x height = h
ganeshie8
  • ganeshie8
|dw:1433742821286:dw|
ganeshie8
  • ganeshie8
what is the area of that lateral face ?
anonymous
  • anonymous
um h * w
ganeshie8
  • ganeshie8
w = x here right
anonymous
  • anonymous
yes
ganeshie8
  • ganeshie8
since the box has four lateral faces, the lateral area is simply \(4*xh\)
ganeshie8
  • ganeshie8
so do you get how i arrived at the surface area equation \((1)\)
anonymous
  • anonymous
oh ok yea
ganeshie8
  • ganeshie8
the expression for volume would be \[V = x*x*h = x^2h\tag{2}\]
ganeshie8
  • ganeshie8
solve \(h\) from first equation and plug it in abvoe
anonymous
  • anonymous
so what does the open top do ?
ganeshie8
  • ganeshie8
it does nothing, do you have "h" from first equation ?
ganeshie8
  • ganeshie8
from first equation, \[x^2+4xh=2700\\~\\\implies 4xh=2700-x^2\\~\\\implies h = \frac{675}{x}-\frac{x}{4}\] yes ?
anonymous
  • anonymous
h=V/x2
anonymous
  • anonymous
okey yea i tryed it and my final answer is 135000 , what u get ?
ganeshie8
  • ganeshie8
do you mean 13500 ? http://www.wolframalpha.com/input/?i=maximize+x*%282700-x%5E2%29%2F4%2Cx%3E0
anonymous
  • anonymous
oh sorry yea
anonymous
  • anonymous
so the open top is just for confusing ?
anonymous
  • anonymous
i should ignore it the next time i see it ?
ganeshie8
  • ganeshie8
what do you mean you should ignore it
ganeshie8
  • ganeshie8
the surface area changes if it was not open top
anonymous
  • anonymous
how would it look like then ?

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