SOLUTION: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then fo

Algebra ->  Functions -> SOLUTION: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then fo      Log On


   

Question 342277: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.
Found 2 solutions by ankor@dixie-net.com, nyc_function:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A box with an open top is to be constructed from a rectangular piece of cardboard
with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each
corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.
:
Let x = side of the square
then the box dimensions (Length,Width,Height) will be:
(18-2x) by (30-2x) by x
Vol = (18-2x)*(30-2x)*x
V = (540 - 36x - 60x + 4x^2)* x
The volume as a function of x
V(x) = 4x^3 - 96x^2 + 540x

Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
The width will be 18 - 2x, the length 30 - 2x and the height x
V = x(18-2x)(30 - 2x)
You can now use the FOIL method to expand your function.
I'll let you that.