Question

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 A of the cross section of the column is $(81\pi )m^2$ .

Step-by-step explanation:

Here we have , building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18π, pi meters. We need to find What is the area A of the cross section of the column .Let's find out:

We know that  , Circumference of circle = $2\pi r$

⇒ $Circumference = 2\pi r$

⇒ $18\pi= 2\pi r$

⇒ $\frac{18\pi}{2\pi }= \frac{2\pi r}{2\pi }$

⇒ $\frac{18\pi}{2\pi }=r$

⇒ $r=9$

We know that area of circle = $\pi r^2$

⇒ $Area= \pi r^2$

⇒ $Area= \pi 9^2$

⇒ $Area= 81\pi$

Therefore , the area A of the cross section of the column is $(81\pi )m^2$ .