Question

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Find the radius of a circle where the area of the circle equals the circumference of the circle.

Answer 1

Set up and equation
Circumference = area
2pi•r = pi•r^2
Solve for r
2pi/pi = r^2/r
2=r

Answer 2

Answer: Radius = 2

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Step-by-step explanation:

For a circle with radius r, we have these formulas

• area = pi*r^2
• circumference = 2*pi*r

Equate the two expressions and isolate r

pi*r^2 = 2*pi*r

pi*r^2 - 2*pi*r = 0

pi*r(r - 2) = 0

pi*r = 0 or r - 2 = 0

r = 0 or r = 2

A radius of 0 doesn't make much sense, so we ignore it. The only possible answer is r = 2.

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If the radius is 2, then,

• area = pi*r^2 = pi*2^2 = pi*4 = 4pi
• circumference = 2*pi*r = 2*pi*2 = 2*2*pi = 4pi

Both result in 4pi to help confirm our answer.