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?

Answer 1

`A=81\pi\ m^2`

Explanation:

step 1

Find the radius of the circular cross section

The circumference is given by the formula

`C=2\pi r`

we have

`C=18 \pi\ m`

substitute

`18 \pi=2\pi r`

solve for r

simplify

`r=9\ m`

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

`A=\pi r^(2)`

we have

`r=9\ m`

substitute

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

`A=81\pi\ m^2`