Question 644110: A box with an open top is constructed from a rectangular piece of cardboard which is initially 20 inches long and 15 inches wide. The box will be formed by removing squares of length x inches from each corner and then folding up the sides (as shown below). Express the volume (V) of the box as a function of x.
So I know that volume of a rectangle is A=lwh and that I probably need to find out the perimeter to get the sides? And then I think there's going to be an 8x used in there for all the squares they're taking out? I'm real confused, my teacher really can't teach our class well, literally the whole lecture hall frowns upon her lack of teaching skills.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A box with an open top is constructed from a rectangular piece of cardboard
which is initially 20 inches long and 15 inches wide.
The box will be formed by removing squares of length x inches from each
corner and then folding up the sides (as shown below).
the volume (V) of the box as a function of x.
:
Removing the squares will give us an open box with the dimensions:
(20-2x) by (15-2x) by x
Vol = L * W * H
FOIL the length and width
V(x) = (300 - 40x - 30x + 4x^2)*x
which is:
V(x) = 4x^3 - 70x^2 + 300x; the volume as a function of x
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