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

2 Answers
Oct 1, 2015

Answer:

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#

Oct 1, 2015

Answer:

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)#