Question

This may be simple, but I'm not getting it. An open box of maximum volume is to be made from a square piece of material, 24cm on a side, by cutting equal squares from the corners and turning up the sides. The table for it is:
Height(x) Volume(V)
1 484
2 800
3 972
4 1024
5 960
6 864
If volume,V, is a function of x write the function and its domain.

Answer 1

The table should be:
1, 484
2, 800
3, 972
4, 1024
5, 960
6, 864
Sorry!

Answer 2

volume= x^3 domain is 0<x<24cm

Answer 3

height x
length = 24 - 2x
width = 24 - 2x

volume = x(24-2x)(24-2x)
v = x(576 - 96 x + 4 x^2)
v = 4 x^3 -96 x^2 + 576 x

now x may not be negative
x may not be equal to or greater than 12 or there is no box bottom left
so
0 < x <12