Question

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

Answer 1

Answer:

$A=81\pi\ m^{2}$

Step-by-step 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

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

$A=81\pi\ m^{2}$