SOLUTION: A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 inches wide. The box will be formed by removing squares of leng
Question 567351: A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 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.
I've been trying to figure out this problem for a while, any help is greatly appreciated!!! Thanks! 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 30 inches long and 23 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.
:
From the information, the box dimensions will be:
(30-2x) by (23-2x) by x (Height)
:
therefore the volume:
V(x) = x*(30-2x)*(23-2x)
FOIL
V(x) = x(690 - 60x - 46x + 4x^2)
;
which is usually written
V(x) = x(4x^2 - 106x + 690)
;
multiply by the height
V(x) = 4x^3 - 106x^2 + 690x
