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A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18 pi meters.
What is the area A of the cross section of the column? Give your answer in terms of pi.

A=◻

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is $18 \pi \text{ meters}$ . What is the area $\newline$ $A$ of the cross section of the column? Give your answer in terms of $\pi$ . $\newline$ $A=\square$

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Area of quadrilaterals and triangles: word problems

Full solution

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

18 \pi \text{ meters}

. What is the area

\newline

A

of the cross section of the column? Give your answer in terms of

\pi

.

\newline

A=\square

Find Radius: Step $1$ : Find the radius of the circle using the circumference formula. $\newline$ Circumference formula: $C = 2\pi r$ , where $C$ is the circumference and $r$ is the radius. $\newline$ Given $C = 18\pi$ meters. $\newline$ Set up the equation: $18\pi = 2\pi r$ . $\newline$ Solve for $r$ : $r = \frac{18\pi}{2\pi} = 9$ meters.
Calculate Area: Step $2$ : Calculate the area of the circle using the radius. $\newline$ Area formula: $A = \pi r^2$ , where $A$ is the area and $r$ is the radius. $\newline$ Substitute $r = 9$ meters into the formula: $A = \pi(9)^2 = 81\pi$ square meters.

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