Finding circumference of a circle when given the area

if we know some circle has an area of 36 pi so it has an area of 36 PI 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 36 pi 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 we do in a different color so we could set up an equation PI R squared is equal to 36 pi now if we want to solve for the radius the first thing that mean 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 okay if 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 our circumference circumference is equal to 2 PI R and in this case R is equal to 6 so it's equal to 2 pi times 2 pi times 6 which is going to be equal to 12 12 pi so that's straightforward area 36 pi 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 12 pi