<PRE><B>Question 458113</B>
A square piece of cardboard is 6 inches on a side.
 A square piece x inches on a side is cut out from each corner.
 The flaps are then turned up to form an open box.
 Find polynomials that represent the volume and outside surface area of the box.
:
Cutting the squares from each corner will give us box dimensions of:
(6-2x) by (6-2x) by x 
Volume
v = x(6-2x)(6-2x)
FOIL
v = x(36-12x-12x+4x^2)
v = x(36-24x+4x^2)
v = 36x - 24x^2 + 4x^3
V(x) = 4x^3 - 24x^2 + 36x, represents the volume
:
Surface area
S.A. = 4(x(6-2x)) + (6-2x)^2
S.A. = 4(6x - 2x^2) + (4x^2 - 24x + 36
S.A. = 24x - 8x^2 + 4x^2 - 24x + 36
Combine like terms
S.A = -8x^2 + 4x^2 + 24x - 24x + 36
S.A = -4x^2 + 36. represents the surface area without the top
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