.
A box with a square base and no top is to be made from a square piece of carboard
by cutting 2 in. squares from each corner and folding up the sides.
The box is to hold 6050 in3. How big a piece of cardboard is needed?
~~~~~~~~~~~~~
Let x be the side length (the dimension) of the square cardboard.
After cutting 2 in. squares at the corners of the cardboard and folding,
the base of the box has dimensions (x-4) inches by (x-4) inches.
The volume of the box is then 2*(x-4)^2, so we have this equation for x
2*(x-4)^2 = 6050.
It implies
(x-4)^2 = 6050/2 = 3025
x-4 = = 55 inches.
Hence, x = 55 + 4 = 59 inches.
ANSWER. The cardbox should be 59 x 59 inches.
Solved.