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 us assume side of initial square be x. Now, after cutting squares of 3in from the corners and making a box by folding the sides, will form a box of volume = (x-6)(x-6)(3).
So, (x-6)(x-6)(3)=243
(x-6)(x-6)=81
x-6=9
x=15in.