Question

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

Answer 1

We first find the radius from `P=2pir`, also equal to `8pi`

Explanation:

`r=(8pi)/(2pi)=4`

Now the area is:

`A=pir^2=pi*4^2=16pi`

Answer 2

Area `=16pi` 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]`color(white)("XXX")C=pid rarr d=C/pi`

[2]`color(white)("XXX")r = d/2`

[3]`color(white)("XXX")A=pir^2`

Given `C=8pi`

from [1] we have:
[4]`color(white)("XXX")d=8`

from [2] and [4] we have:
[5]`color(white)("XXX")r=4`

from [3] and [5] we have
[6]`color(white)("XXX")A=pi(4)^2 = pi16 (=16pi)`