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Question 708735: A closed rectangular box is of uniform thickness x inches. The box has outer dimensions 6 inches, 4 inches and 3 inches and it has an inside volume of 30 cubic inches. Find x.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Volume (V)=Length(L)*Width(W)*Height(H) or V=LWH
If the box has a uniform thickness of x inches, then the inside dimensions are:
L=(6-2x), W=(4-2x), H=(3-2x)
Soooo
(6-2x)(4-2x)(3-2x)=30 when we simplify this, we get:
8x^3-52x^2+108x-42=0
This is a cubic equation and there are several methods for solving cubic equations and most all are quite involved. There are also cubic equation calculators that allow you to plug in the coefficients and they will calculate the answers.
But there's another way to solve this problem:
Assume x=1 inch
V=4*2*1=9 cu in----inside volume is far too small
Assume x=1/4 inch
V=(5.5)*(3.5)*(2.5)=48.125 inside volume is much too large
Assume x=3/4 inch
V=(4.5)*(3.5)*(1.5)=23.625 inside volume is too small
Assume x=1/2 inch
V=5*3*2=30 ---BINGO!!!!!
Hope this helps---ptaylor
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