# What is the area of a circle with a circumference of 8(pi) inches?

Oct 1, 2015

We first find the radius from $P = 2 \pi r$, also equal to $8 \pi$

#### Explanation:

$r = \frac{8 \pi}{2 \pi} = 4$

Now the area is:

$A = \pi {r}^{2} = \pi \cdot {4}^{2} = 16 \pi$

Oct 1, 2015

Area $= 16 \pi$ square inches

#### Explanation:

Defining:
color(white)("XXX")C = " circumference"
color(white)("XXX")A = " area"
color(white)("XXX")d = " diameter"
color(white)("XXX")r = " radius"

The key formulas are:
[1]$\textcolor{w h i t e}{\text{XXX}} C = \pi d \rightarrow d = \frac{C}{\pi}$

[2]$\textcolor{w h i t e}{\text{XXX}} r = \frac{d}{2}$

[3]$\textcolor{w h i t e}{\text{XXX}} A = \pi {r}^{2}$

Given $C = 8 \pi$

from [1] we have:
[4]$\textcolor{w h i t e}{\text{XXX}} d = 8$

from [2] and [4] we have:
[5]$\textcolor{w h i t e}{\text{XXX}} r = 4$

from [3] and [5] we have
[6]$\textcolor{w h i t e}{\text{XXX}} A = \pi {\left(4\right)}^{2} = \pi 16 \left(= 16 \pi\right)$