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 ->  Rectangles -> 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 227484: 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
If squares with a side x, are removed from each corner, the dimensions of the box:
(30-2x) by (18-2x) by x
:
V = H * L * W
:
V = x*(18-2x)*(30-2x)
FOIL
V = x(540 - 36x - 60x + 4x^2)
:
V = x(4x^2 - 96x + 540)
:
V(x) = 4x^3 - 96x^2 + 540x