Question

The circumference of a circle is 7π.What is its area?

Answer 1

Given

The circumference of a circle is 7π

We need to find the area.

First of all, let's use the formula for the circumference of a circle and find the radius. Shown below:

`\begin{gathered} \text{Circumference}=2\pi r \\ C=2\pi r \\ 7\pi=2\pi r \\ r=(7\pi)/(2\pi) \\ r=(7)/(2) \end{gathered}`

Now, we can easily find the area by using this radius value in the formula for the area of a circle. Shown below:

`\begin{gathered} \text{AreaofCircle}=\pi r^2 \\ A=\pi r^2 \\ A=\pi((7)/(2))^2 \\ A=\pi((49)/(4)) \\ A=(49\pi)/(4) \end{gathered}`

Thus, the exact area of the circle is:

`(49\pi)/(4)`