Answer
Circumference(C) of a circle is given by:
[tex]C = 2\pi r[/tex]
where r is the radius and value of [tex]\pi = 3.14[/tex]
As per the given statement:
A building engineer analyzes a concrete column with a circular cross section.
The circumference of the column is [tex]18 \pi[/tex] meters.
then;
[tex]18 \pi= 2\pi r[/tex]
Divide both sides by [tex]2 \pi[/tex] we have;
9 = r
or
r = 9 meters
We have to find the area of the cross section of the column
Area of a circle is given by:
[tex]A = \pi r^2[/tex]
then;
[tex]A = \pi \cdot 9^2 = 81 \pi[/tex] meter square.
therefore, the area A of the cross section of the column is [tex]81 \pi[/tex] meter square.
The area of the concrete column that has a circumference of 18π is 81π.
The circumference of the circle is the outer boundary of the circle also known as the perimeter of a figure. It is given by the formula,
[tex]C=2\pi r[/tex]
where r is the radius of the circle.
The area of a circle is given by the formula,
[tex]\rm Area=\pi r^2[/tex]
where r is the radius of the circle.
we will use the circumference formula of the circle,
[tex]C=2\pi r\\\\18\pi = 2 \pi r\\\\r = \dfrac{18 \pi}{2 \pi}\\\\r = 9[/tex]
We will use the formula of area of the concrete column,
[tex]\rm Area=\pi r^2[/tex]
[tex]\rm Area=\pi (9)^2[/tex]
[tex]\rm Area=81 \pi[/tex]
Hence, the area of the concrete column is 81π.
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