Question

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18π meters.

What is the area A of the cross section of the column?
Give your answer in terms of pi.

Answer 1

`A=81\pi\ m^(2)`

Explanation:

Step 1

Find the radius of the circular cross section

we know that

The circumference is equal to

`C=2\pi r`

we have

`C=18\pi\ m`

substitute and solve for r

`18\pi=2\pi r`

simplify

`18=2 r`

`r=9\ m`

Step 2

Find the area of the circular cross section

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=9\ m`

substitute

`A=\pi (9)^(2)`

`A=81\pi\ m^(2)`