SOLUTION: A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed from each corner in order to form a rectangular box. If the volume of the box is to be a maximum what i

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Question 173211: A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed from each corner in order to form a rectangular box. If the volume of the box is to be a maximum what is the value of X?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed
from each corner in order to form a rectangular box.
If the volume of the box is to be a maximum what is the value of X?
:
From the given information we know the dimensions (L,W,H) of the box is:
(32-2x) by (22-2x) by x
:
Area = length * width * height
A = (32-2x) * (22 - 2x) * x
FOIL
A = x(704 - 64x - 44x + 4x^2)
A = x(704 - 108x + 4x^2)
A = 704x - 108x^2 + 4x^3
or the standard arrangement is:
y = 4x^3 - 108x^2 + 704x
:
Plot this equation, we only are interested in the positive values x,y values
+graph%28+300%2C+200%2C+-6%2C+15%2C+-500%2C+1600%2C+4x%5E3-108x%5E2%2B704x%29+
:
Using my trusty Ti83, max volume occurs when x = 4.274 cm about 1348 cu/cm