What is the radius of a circle when the numeric values of the circumference and the area are equal?

Answer 1

C = 2 pi r
A = pi r^2

So when you equate these you get:
2 pi r = pi r^2

Divide both sides by pi and by r:
2 = r

So the radius of 2 will give an area of 4 pi and a circumference of 4pi.

Answer:
r = 2

Answer 2

Wow, everybody so far has gotten it half right. :)

Actually everyone has the right idea, they just didn't give the "obvious" answer. So, let's follw their game plan and see what happens. You want the area numerically equal to the circumference and the value of the radius that accomplishes that. So,

pir^2 = 2pir --now rearrange
pir^2 - 2pir = 0 --now divide both sides by pi
r^2 - 2r = 0 -- now factor
r(r - 2) = 0 -- now the product is 0 whenever either of the factors (or both) are 0

r - 2 = 0 give r = 2 --which everyone got, but the other answer is when r = 0.

There are two solutions r = 2 and r = 0

HTH

Charles

Answer 3

Good Luck

2 pi r = pi r^2

r = 2

Answer 4

Solve for r in r^2=2 times pi times r.
r=radius.

Answer 5

so area of a circle (pi*r^2) = circumference of a circle (2*pi*r)
so solve pi*r^2 =2Pi*r
r^2=2r
r^2-2r =0
r(r-2)=0
r=0 or r=2
can't be 0 must be 2
check it pi*2^2=4pi
2*pi*2=4pi also

Answer 6

2 pi r = pi r^2
cancel one r and the pi
r = 2

Answer 7

2 pi r = pi r^2

r = 2

Answer 8

2pi*r=pi*r^2

r=2