<PRE><B>Question 365065</B>
squares are cut from the corners of a rectangle sheet of metal 30 in by 50 in.
 the four sides are then turned up and soldered.
 how large are the squares if the volume of the resulting open metal box is
 2,392 cubic inches?
:
Let x = length of the side of the 4 squares removed
:
Then the dimensions of the open box will be:
L = 50-2x
W = 30-2x
H = x
:
Volume of the box; L*W*H:
(50-2x)*(30-2x)*x = 2392 cu/in
FOIL
(1500 - 100x - 60x + 4x^2)*x = 2392
:
x(4x^2 - 160x + 1500) = 2392
:
4x^3 - 160x^2 + 1500x - 2392 = 0
Simplify, divide by 4
x^3 - 40x^2 + 375x - 598 = 0
Plot this equation (Red)
x = 2 inches is the reasonable solution
:
4000 cu inches
x^3 - 40x^2 + 375x - 1000
plot this equation also (green)
x = 5 inches, but we have two reasonable solutions
or
x = 7 inches

{{{ graph( 300, 200, -4, 15, -600, 600, x^3 - 40x^2 + 375x - 598, x^3 - 40x^2 + 375x - 1000) }}}





</PRE>