Answer:
[tex]\$527.2[/tex]
Step-by-step explanation:
[tex]r_i[/tex] = Inner radius
Inner circumference = 4.5 m
[tex]2\pi r_i=4.5\\\Rightarrow r_i=\dfrac{4.5}{2\pi}\\\Rightarrow r_i=\dfrac{2.25}{\pi}[/tex]
[tex]r_o[/tex] = Outer radius
Outer circumference = 4.6 m
[tex]2\pi r_o=4.6\\\Rightarrow r_o=\dfrac{4.6}{2\pi}\\\Rightarrow r_o=\dfrac{2.3}{\pi}[/tex]
h = Height of cylindrical pipe = 8 m
Total surface area to be painted
[tex]s=\pi r_i^2h+\pi r_o^2h\\\Rightarrow s=\pi h(r_i^2+r_o^2)\\\Rightarrow s=\pi\times 8((\dfrac{2.25}{\pi})^2+(\dfrac{2.3}{\pi})^2)\\\Rightarrow s=26.36\ \text{m}^2[/tex]
Cost of painting 1 square meter is 20
Cost of painting the inner and outer surfaces is [tex]20\times 26.36=\$527.2[/tex]
The total cost painting the surfaces is [tex]\$527.2[/tex].
