Question

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

8778 cubic units
8558 cubic units
8448 cubic units
8668 cubic units

Answer 1

`V=8,448u^3`

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)=(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)=(6*8u*16u)/(2)\\ \\A_(b)=(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