Question

a box is to be made by cutting out the corners of a square piece of cardboard and folding the edges up. if 3-inch squares are to be cut out of the corners and the box contains 243 cubic inches, what is the length of a side of the original cardboard square

Answer 1

let the base be x by x
after cut out, base is (x-3) by (x-3) and the height is 3

3(x-6)(x-6) = 243
(x-6)^2 = 81
x-6 = ±9
x = 15 or x is a negative which would make no sense

so the base was 15 by 15 inches

check:
after cutting out 3 inches from each end, the base is 9 by 9
volume = 9x9x3 = 243