Radius & diameter from circumference

let's say that we know that the circumference circumference of a circle is 49 pi based on that let's see if we can figure out what the radius of that same circle is going to be and I encourage you and I'll write equals here and I encourage you to pause the video and see if you can figure it out on your own so let's just draw the circle to help visualize it so I'm going to do a hand-drawn circle clearly not a perfect circle right over here and we know that if it's radiuses of length R that the circumference the circumference is going to be 2 pi times R so I could write the circumference is equal to 2 pi times R in fact the number pi the number pi the standard definition for it is just the ratio between the circumference and the diameter of a circle now why is that well let's just if the diameter here the diameter here is 2r all right we have R and then I have another R we see that the circumference is pi times 2r or we can say that the ratio between the circumference and the diameter the ratio between the circumference and the diameter which is the ratio between C and 2r well that's just going to be that's just going to be pi well anyway this was I've gone on longer than I need to just to solve this problem so we can go to this original formula here saying that circumference is 2 pi times R and we can just substitute in 49 pi for the circumference so we could say 49 pi is going to be equal to 2 pi times the radius 2 pi times the radius now let's see we can divide both sides by 2 pi to solve for R so dividing both sides by 2 pi on the right hand side the 2 PI's cancel out on the left hand side pi divided by pi cancels out 49 divided by 2 is 24 0.5 so if the circumference is 49 pi whatever units then the radius is going to be 24 0.5 those units let's do one more of these let's say that we have a circle whose circumference I'll just say C is equal to 1600 pi my question is what is the diameter the diameter of the circle is equal to what well just as we said that the circumference could be written as 2 pi R or as pi times 2 R 2 R is just the diameter so we could say that the circumference is equal to PI times the diameter and once again that comes out of that that traditional definition of pi is the ratio between the circumference of the diameter you could say that the ratio between the circumference of the diameter is equal to pi it's you know circles are this very fundamental thing in the universe and you take the ratio of the circumference in the diameter you get this magical and mystical number that we see that keeps popping up in mathematics but anyway back to the problem if we say the circumference is 1,600 pi 1,600 pi and this is equal to pi times the diameter well we can just divide both sides by PI divide both sides by PI to get the diameter which is going to be 1600 so circumference is 1600 PI units whatever units those are may be meters then the diameter is just going to be 1,600 of those units or in this case may be meters and we're all done