The table should be:
1, 484
2, 800
3, 972
4, 1024
5, 960
6, 864
Sorry!
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.
3 answers
volume= x^3 domain is 0<x<24cm
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
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