Answer:
[tex]V=8,448u^3[/tex]
Step-by-step explanation:
The volume of a prism is given by:
[tex]V=A_{b}*h[/tex]
where [tex]A_{b}[/tex] is the area of the base, and [tex]h[/tex] is the height of thr prism.
We know that the height is:
[tex]h=22[/tex]u
and the bases of this prism are hexagons.
Thus the area of the base is the area of a regular hexagon:
[tex]A_{b}=\frac{n*l*a}{2}[/tex]
where [tex]n[/tex] is the number of sides: for an hexagon: [tex]n=6[/tex]
[tex]l[/tex] is the length of each side: [tex]l=8[/tex]u,
and [tex]a[/tex] is the apothem: [tex]a=16u[/tex]
we substitute all of this to find the area of the base:
[tex]A_{b}=\frac{6*8u*16u}{2}\\ \\A_{b}=\frac{768u^2}{2}\\ \\A_{b}=384u^2[/tex]
and finally we use the formula for the volume:
[tex]V=A_{b}*h[/tex]
we get the following:
[tex]V=384u^2*22u\\V=8,448u^3[/tex]
which is the third option
