Answer:
The box could be 9 x 9 x 12 or 12 x 12 x 6.75
Step-by-step explanation:
There are lots of possibilities. If you want a square bottom, you can use a formula like [tex]V=x^{2} y[/tex]
If you have a given volume, put it in for V. If you know the size of the bottom put it in for x. I selected 9 for the x value because I know that 972 is divisible by 9. (If the sum of the digits is divisible by 9, the number is divisible by 9)
So 0 squared is 81. 972 ÷ 81 = 12 so that is the height of the sides.
if you want a shallower box, use a larger base. 12×12=144 972÷144=6.75
Doing this on a graphing calculator is fun and yields nearly infinite possibilities. You can graph[tex]x^{2} y=V[/tex] and [tex]y = h[/tex] and see where the lines intersect.
Enjoy!
