Answer:
The total cost is $4825.19.
Explanation:
Given information:
Base edge = 8 ft
Height = 75 ft
The surface area of a regular hexagonal pyramid is
[tex]Area=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}}[/tex]
where, a is base edge and h is height.
Substitute a=8 and h=75 in the above formula.
[tex]Area=\frac{3\sqrt{3}}{2}(8)^2+3(8)\sqrt{(75)^2+\frac{3(8)^2}{4}}[/tex]
[tex]Area=\frac{3\sqrt{3}}{2}(64)+3(8)\sqrt{5625+48}[/tex]
[tex]Area\approx 166.28+1807.66[/tex]
[tex]Area\approx 1973.94[/tex]
The area of regular hexagonal pyramid is 1973.94 sq. ft.
We know that
1 sq. yard = 9 sq. ft
The area of regular hexagonal pyramid in square yard is
[tex]\frac{1973.94}{9}\approx 219.3267[/tex]
It is given that cost of paint is 22 dollars per sq. yard. So, total cost is
[tex]\text{Total cost}=219.3267\times 22=4825.1874\approx 4825.19[/tex]
Therefore the total cost is $4825.19.
