Find radius of a circle so that its area and circumference have same value

Question

directrix · Answer

Write the formula for the area of a circle.
Write the formula for the circumference of a circle.
Set the two formulas equal and solve the resulting equation for r.

anonymous · Answer

Let r, C and A be the radius, circumference and area of the circle.
Then C = 2pir and A = (pi)r^2
But C = A
Hence, 2pir = (pi)r^2
           (pi)r^2 - 2pir = 0
           (pi)r(r - 2) = 0 
Either (pi)r = 0 or r - 2 = 0
Hence, r = 0 units or r = 2 units

directrix · Answer

Good work on the Algebra. Of the two answers, r = 2 is the answer applicable to this problem. I suppose a person could consider that a point is a degenerate circle with radius 0 but I'd go with 2 for the answer.

anonymous · Answer

ok. Thank you.

directrix · Answer

You did all the work. Glad to help.