Question

The circumference of a circle is 24π in. What is the area, in square inches? Express your answer in terms of π.

Answer 1

Given

`circumference\text{ of circle = 24}\pi\text{ in}`

Recall that the formula for the circumference of a circle C is:

`C\text{ = 2}\pi r`

Using the formula, we can find the radius of the circle as shown:

`\begin{gathered} 2\pi r\text{ = 24}\pi \\ Divide\text{ both sides by 2}\pi \\ r\text{ = }(24\pi)/(2\pi) \\ r\text{ = 12 in} \end{gathered}`

The area A of a circle can be found using the formula:

`A\text{ = }\pi r^2`

Substituting the value obtained:

`\begin{gathered} A\text{ = }\pi\text{ }*\text{ 12}^2 \\ =\text{ 144}\pi\text{ in}^2 \end{gathered}`

The area is 144π square in