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A box has a square base; the height is 7 more than the side lengths of the base. The volume of the box is 4000 cubic inches. How high is the box? (answers within 0.2 of the exact answer will be accepted).

 Jul 10, 2018
 #1
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The volume of the box  is  L * W * H.....but..... L and  W are the same  = the side lengths

So...let the side lenghts  = S

And  the height is   S  + 7

 

So...we have that

 

S * S * (S + 7)   = 4000       simplify

 

S^3  + 7S^2   = 4000

 

S^3  + 7S^2  -  4000   = 0

 

We can obtain a graphical solution here :

 

https://www.desmos.com/calculator/51gbh74ttk

 

The graph shows that the side length  ≈  13.85  in

 

But the height  is 7 more  ≈  20.85  in

 

 

cool cool cool

 Jul 10, 2018

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