SOLUTION: Find the area of a circle whose circumference is 1/3

Question 356749: Find the area of a circle whose circumference is 1/3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c = 2*pi*r is the formula for the circumference of a circle.

since c = 1/3, this means that:

1/3 = 2*pi*r

divide both sides of this equation by 2*pi to get:

r = 1/(6*pi)

a = pi*r^2 is the formula for the area of a circle.

since r = 1/(6*pi), then:

r^2 = (1/(6*pi)^2 = (1^2) / (6*pi)^2 = 1 / (36*pi^2)

since a = pi*r^2, substitute for r^2 to get:

a = pi*(1/(36*pi^2) which is the same as (pi/(36*pi^2) which simplifies to:

a = 1 / (36*pi)

we can solve backwards to find r again.

a = pi * r^2

this makes (1/(36*pi) = pi*r^2

if we multiply both sides of this equation by pi, we get:

1/36 = pi^2 * r^2

if we take the square root of both sides of this equation, we get:

1/6 = pi*r

if we multiply both sides of this equation by 2, we get:

1/3 = 2*pi*r

we worked our way back from the area equation to the circumference equation, so we should be good.

your answer should be:

a = 1 / (36*pi)
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