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Inessa05 [86]
3 years ago
7

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

Mathematics
1 answer:
OverLord2011 [107]3 years ago
8 0

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=22u

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=8u,

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

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