SOLUTION: A container with a square base, vertical sides, and open top is to be made from 1000 ft2 of material. (a) Write an equation for the volume of the con- tainer as a function of t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A container with a square base, vertical sides, and open top is to be made from 1000 ft2 of material. (a) Write an equation for the volume of the con- tainer as a function of t      Log On

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Question 388733: A container with a square base, vertical sides,
and open top is to be made from 1000 ft2 of material.
(a) Write an equation for the volume of the con-
tainer as a function of the length of a side of
the base.
(b) Write an equation for the volume of the con-
tainer as a function of the length of the ver-
tical side
I can do part (a) but I am stuck on (b), Help would be greatly appreciated. Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
The square base can be any size, so I'll call
the sides of the base x.
I want the 1000 ft2 of material to be a
square also, so the sides of the container will
all be the same height .
that means each side of the material will be
10%2Asqrt%2810%29 ft2
I'll place the x%5E2 ft2 base exactly in the center.
That means the 4 sides will measure x by %2810%2Asqrt%2810%29+-+x%29%2F2
Let V = volume
V+=+x%5E2%2A%2810%2Asqrt%2810%29+-+x%29%2F2
V+=+5%2Asqrt%2810%29%2Ax%5E2+-+x%5E3%2F2
Is this what you got?
(b)
I'll call the length of the vertical side y
y+=+%2810%2Asqrt%2810%29+-+x%29%2F2
Ok, now I can say that
V+=+x%5E2%2Ay
Now I just have to find x in terms of y,
so I go back to y+=+%2810%2Asqrt%2810%29+-+x%29%2F2
2y+=++10%2Asqrt%2810%29+-+x
x+=+10%2Asqrt%2810%29+-+2y
Now I can say
V+=+%2810%2Asqrt%2810%29+-+2y%29%5E2+%2Ay
V+=+%281000+-+40%2Asqrt%2810%29%2Ay+%2B+4y%5E2%29%2Ay
V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y
Check answer:
Suppose y+=+1
That would mean x+=+10%2Asqrt%2810%29+-+2
V+=+1%2A%281000+-+40%2Asqrt%2810%29%29+%2B+4
V+=+1004+-+40%2Asqrt%2810%29
The equation gives me:
V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y
V+=+4+-+40%2Asqrt%2810%29+%2B+1000
same answer