A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from

Question

each corner, and the ends and sides are turned up to make an open box. If the volume of the box is
2760 cubic inches, what were the original dimensions of the rectangular piece of tin? Show the work
that leads to the answer.
Length, width, and height must be positive. Use this fact to find the domain of the volume function V(x)
in the form a < x < b. Explain. Justify your explanation by solving inequalities.

Answer 1

xy = 1334, so y = 1334/x

3(x-6)(y-6) = 2760
3(x-6)(1334/x - 6) = 2760
solve that and you get
x = 29 or 46

so, the original sheet was 29 by 46 in.

v(x) = (24012+4110x-18x^2)/x
= 6(x-6)(667-3x)/x

for v>0, we have 6 < x < 667/3

Makes sense, since we can't cut two 3" corners if the side length is less than 6.

And if x is too big, there's not anything left for y.