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## Area and circumference challenge problems

# Finding circumference of a circle when given the area

CCSS.Math:

## Video transcript

If we know some circle
has an area of 36pi-- so it has an area
of 36pi-- can we figure out what the
circumference of this circle is? And I encourage you
to pause this video, and try to think
about that question. Well, from the area, we could
figure out what the radius is, and then from that
radius, we can figure out what its circumference is. So we know that the
area, which is 36pi, is equal to pi r squared. And so if you look at it on
both sides of this equation, if we divide-- let me rewrite
it so it's a little bit clearer in a different color. So we could set up an equation
pi r squared is equal to 36pi. Now, if we want to
solve for the radius the first thing that
we might want to do is divide both sides by pi. Then, we're left with r
squared is equal to 36. Now, if we just solve this
as a pure math equation, you might say, OK, we could
take the positive and negative square root of 36. r could be plus
or minus 6, but we need to remember
that r is a distance, so we only care
about the positive. So if we take the principal root
of 36, we get r is equal to 6. From there, we can use this to
figure out the circumference. So the circumference
is equal to 2 pi r. Circumference is
equal to 2 pi r. And in this case,
r is equal to 6. So it's equal to 2
pi times 6, which is going to be equal to 12pi. So that's straightforward,
area 36pi, we leverage pi r squared to figure out
that the radius was 6, and then from that we
were able to figure out that the circumference was 12pi.