Question

The circumference of a circle is 15pi in. What is the area, in square inches? Expressyour answer in terms of pi

Answer 1

Given: The circumference of a circle as

`Circumference(circle)=15\pi in`

To Determine: The area of the circle

Solution

The formula for finding the circumference of a circle is

`\begin{gathered} Circumference(circle)=2\pi r \\ So \\ 2\pi r=15\pi in \\ r=(15\pi)/(2\pi)in \\ r=7.5in \end{gathered}`

Since we have the radius, we can calculate the area using the formula below

`\begin{gathered} Area(circle)=\pi r^2 \\ =\pi((15)/(2))^2in^2 \\ =(225)/(4)\pi in^2 \\ =56.25\pi in^2 \end{gathered}`

Hence, the area of the square is 56.25pi square inches OR 225/4 square inches