Question

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18 \pi18π18, pi meters.
What is the area AAA of the cross section of the column?
Give your answer in terms of pi.

Answer 1

The area of the cross section of the column is $18 \pi \ m^2$

Explanation:

Given that a building engineer analyzes a concrete column with a circular cross section.

Also, given that the circumference of the column is $18 \pi$ meters.

We need to determine the area of the cross section of the column.

The area of the cross section of the column can be determined using the formula,

$Area= \pi r^2$

First, we shall determine the value of the radius r.

Since, given that circumference is $18 \pi$ meters.

We have,

$2 \pi r=18 \pi$

   $r=9$

Thus, the radius is $r=9$

Now, substituting the value $r=9$ in the formula $Area= \pi r^2$, we get,

$Area = \pi (9)^2$

$Area = 81 \pi$

Thus, the area of the cross section of the column is $18 \pi \ m^2$