SOLUTION: when you first walk into weaver there are 2 large regular octogonal pillars. the edges are 6.5 and they are 9 feet tall. how much granite was needed to build these pillars??

Question 148791: when you first walk into weaver there are 2 large regular octogonal pillars. the edges are 6.5 and they are 9 feet tall. how much granite was needed to build these pillars??
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
To solve this problem, you need to know the volume of each pillar. The volume is "area of the base" times "height".
.
"area of the base" = "area of an octagon"
.
Without trying to derive the formula of an octagon, I'll just use it. But, for reference, you might want to check out:
http://www.mathreference.com/geo,hex.html
.
"area of an octagon" = 2(1+sqrt(2))S^2
where S=length of one edge
.
So, plugging in your numbers to:
"area of an octagon" = 2(1+sqrt(2))S^2
"area of an octagon" = 2(1+sqrt(2))6.5^2
"area of an octagon" = 2(1+sqrt(2))42.45
"area of an octagon" = 2(1+1.414)42.45
"area of an octagon" = 2(2.414)42.45
"area of an octagon" = (4.828)42.45
"area of an octagon" = 204 sq ft
.
Now, to get the volume we multiply the area times the height:
"vol of one pillar" = "area of an octagon" * "height of pillar"
"vol of one pillar" = 204 * 9
"vol of one pillar" = 1836 cubic feet
.
Since we have 2 pillars, we multiply the above by 2:
2 * 1836 = 3672 cubic feet
.
That's how much granite you need.

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