Question 356749
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)