Question

The circumference of a circle is 9π ft. What is the area, in square feet? Express your answer in terms of π.

Answer 1

20.25π square feet

Explanation:

The circumference of a circle = 9π ft.

Given any circle of radius, r, its circumference is calculated using the formula:

`C=2\pi r`

Equating the two:

`\begin{gathered} 2\pi r=9\pi \\ \text{ Divide both sides by }2\pi \\ (2\pi r)/(2\pi)=(9\pi)/(2\pi) \\ r=4.5\;ft. \end{gathered}`

Next, we find the area of the circle.

The area of a circle is calculated using the formula:

`Area=\pi r^2`

Substitute the value of the radius, r obtained earlier:

`\begin{gathered} A=\pi*\left((9)/(2)\right)^2 \\ =(81)/(4)\pi \\ =20.25\pi\;square\text{ feet} \end{gathered}`

The area of the circle is 20.25π square feet.