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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