Answer:
[tex]A=81\pi\ m^2[/tex]
Step-by-step explanation:
step 1
Find the radius of the circular cross section
The circumference is given by the formula
[tex]C=2\pi r[/tex]
we have
[tex]C=18 \pi\ m[/tex]
substitute
[tex]18 \pi=2\pi r[/tex]
solve for r
simplify
[tex]r=9\ m[/tex]
step 2
Find the area if the cross section of the column
The area of the cross section is equal to the area of a circle
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=9\ m[/tex]
substitute
[tex]A=\pi (9)^{2}[/tex]
[tex]A=81\pi\ m^2[/tex]
