Question

Can I get some help real quick please? thanks!

Answer 1

This reference gives the formula for the volume of a Hexagonal Pyramid as:

`V = 1/2sqrt3ha^2`

Explanation:

We are given that `a = 23" in"` and `h = 27" in"`.

Substitute these numbers into the formula:

`V = 1/2sqrt3(27" in")(23" in")^2`

`V = sqrt3(7141.5)" in"^3`

Answer 2

`V=12369.441`

Explanation:

First, the area of a generic pyramid is equal to one third the area of the base times the height:

`V=1/3*A_b*h`

we have the height, so we need the area of the base. The area of a regular hexagon is given by:

`A_b=3sqrt(3)/2*a^2`

So when we plug that into the pyramid formula the 3 cancels out with the 1/3 and we get:

`V=sqrt(3)/2*a^2*h`

Now just plug in the numbers:

`V=sqrt(3)/2*23^2*27`

`V=12369.441`