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

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

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

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

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