Answer: Radius = 2
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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.
