Question

a cub measures n inches on each edge. If a slice 1 inch thick is cut from one face of the cube and then a slice 3 inches thick is cut from another face of the cube, the resulting solid has a volume of 1560 cubic inches. Find the dimensions of the original cube.

Answer 1

original side = n
slice = (1)n^2

is the 2nd slice from the other square face, or one of the four nx(n-1) faces?

Assuming the latter, lest the problem be too, too trivial, then the 2nd
slice = 3(n)(n-1)

n^3 - n^2 - 3n(n-1) = 1560
n^3 - 4n^2 + 3n - 1560 = 0
Hmmm. 1560 = 13*12*10
(n-13)(n^2 + 9n + 120)

so, n=13
original volume: 2197
1st slice: 13x13 = 169
2nd slice: 3x13x12 = 468
remaining: 1560