Abuilding engineer analyzes a concrete column with a circular cross section. the circumference of the column is 18 \pi18π18, pi meters. what is the area of the cross section of the column? give your answer in terms of pi.

The area of the cross section is 81pi meters.

Since we are given the circumference, we can write and solve an equation about the diameter.

C = pi(d)
18pi = pi(d)
18 = d

Since the diameter is 18, the radius is half of that or 9 meters.

Now, plug 9 as the radius into the area formula.

A = pi(r^2)
A = pi(9^2)
A = 81pi