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

Answer:

$A=81\pi\ m^2$

Step-by-step 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

$A=\pi (9)^{2}$

$A=81\pi\ m^2$