Question

Find the volume of a regular hexagonal prism with the height of 22 apothem of 16 and a side length of 8

Answer 1

Answer:

$V=8,448u^3$

Step-by-step explanation:

The volume of a prism is given by:

$V=A_{b}*h$

where $A_{b}$ is the area of the base, and $h$  is the height of thr prism.

We know that the height is:

$h=22$u

and the bases of this prism are hexagons.

Thus the area of the base is the area of a regular hexagon:

$A_{b}=\frac{n*l*a}{2}$

where $n$ is the number of sides: for an hexagon: $n=6$

$l$ is the length of each side: $l=8$u,

and $a$ is the apothem: $a=16u$

we substitute all of this to find the area of the base:

$A_{b}=\frac{6*8u*16u}{2}\\ \\A_{b}=\frac{768u^2}{2}\\ \\A_{b}=384u^2$

and finally we use the formula for the volume:

$V=A_{b}*h$

we get the following:

$V=384u^2*22u\\V=8,448u^3$

which is the third option