Can I get some help real quick please? thanks!

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Answer 1 · 2017-08-20T12:12:10

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

#V = 1/2sqrt3ha^2#

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 · 2017-08-20T12:31:16

#V=12369.441#

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#