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).

Guest Jul 10, 2018

#1**+1 **

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

CPhill Jul 10, 2018