Question

A circle has an area of 36 square inchesFind its radius, diameter and exact circumference

Answer 1

The radius is 6 inches

The diameter is 12 inches

The circumference is 12pi inches

Explanation:

We have that the formula for the area of the circle is the following:

`A=\pi\cdot r^2`

Replacing the area and solving for r (radius):

`\begin{gathered} 36\pi=\pi\cdot r^2 \\ r=\sqrt[]{36}=6 \end{gathered}`

The diameter equals the double radius, therefore

`\begin{gathered} d=2\cdot r=2\cdot6 \\ d=12 \end{gathered}`

We calculate the circumference by means of the following formula

`\begin{gathered} c=2\cdot\pi\cdot r \\ c=2\cdot\pi\cdot6 \\ c=12\pi \end{gathered}`