Expert: Paul Klarreich - 11/27/2007

Question
The volume of a box(in cubic inches) is modeld by the equation V+2x^3+x^2-8x-4, where x is measured in inches.  If the height of box is 2x+1 find an expression for the surfae area of the box in terms of x.  What would be the surface area if x=6?

Answer
Questioner:   Keisha Robinson
Category:  Advanced Math
Private:  No
 
Subject:  volume
Question:  The volume of a box(in cubic inches) is modeld by the equation V+2x^3+x^2-8x-4, where x is measured in inches.  If the height of box is 2x+1 find an expression for the surface area of the box in terms of x.  What would be the surface area if x=6?
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Hi, Keisha,

I assume you meant:

V EQUALS  2x^3 + x^2 - 8x - 4   [PROOFREAD!]

The clue here is that
1. V = LWH and
2. If H = 2x+1, AND
3. We can factor V, THEN
we will get L,W, AND
SA = 2LH + 2LW + 2HW

Factor

V = 2x^3 + x^2 - 8x - 4

V = (2x + 1)(x^2 - 4)

V = (2x + 1)(x + 2)(x - 2)

So we can take  H = 2x+1,  L = x+2,  W = x-2.  Then just use

SA = 2LH + 2LW + 2HW

SA = 2(x+2)(2x+1) + 2(x+2)(x-2) + 2(2x+1)(x-2)

I'll leave the rest to you.