[Music] welcome to math with mr j [Music] in this video i'm going to cover how to calculate the circumference of a circle given the radius or diameter so we'll go through one example of each starting with a circle with a given radius now remember the circumference is the distance around a circle so the perimeter of a circle we can either use the formula circumference equals pi d so pi times diameter or circumference equals 2 pi r so 2 times pi times the radius so depending on if you're using the diameter or radius you can use either formula you'll get the same result either way and remember the diameter is twice the radius so that's why we multiply by two with the formula that includes the radius and one more thing to keep in mind before jumping into our example and that is pi pi is the same for all circles it's a constant pi is the ratio of a circle circumference to its diameter so it's the circumference of a circle divided by its diameter let's jump into our example where we have a circle with a given radius of 9 centimeters now the first thing i'm going to do is write out our formula and we're going to use circumference equals 2 pi r so 2 times pi times r and we're using that formula since we are given the radius so circumference equals 2 pi r now we can plug in the radius so circumference equals 2 times pi times the radius of 9 centimeters once we have that 9 plugged in for our radius we can do 2 times 9 which is 18 and for our next step we can write that as circumference equals 18 pi so we put our number in front of the pi symbol now this is one way to write the circumference and this is called writing it in terms of pi meaning we can write our number in front of the pi symbol and put our unit of measure which is centimeters so circumference equals 18 pi and again our unit of measure centimeters this is called writing it in terms of pi another way we can do this is to write our circumference in decimal form using an approximate value of pi since pi is irrational and we're going to use 3.14 so we are going to use pi is approximately 3.14 so that squiggly equal sign that means an approximate value rather than an equal sign which means an exact value so we can write out our formula circumference equals 2 pi r and then we will plug in so circumference is approximately i'll use that approximate symbol because we are using an approximate value of pi so 2 times three point one four times our radius of nine and now we can calculate so circumference is approximately 56 centimeters so 56 and 52 hundredths centimeters so there's how we calculate the circumference of a circle given the radius let's move on to finding the circumference given the diameter for this example we have a circle with a given diameter of 12 feet now the first thing that we're going to do is to write out our formula we're going to use circumference equals pi d pi times diameter since we are given the diameter so circumference equals pi d pi times diameter then we plug in our diameter so circumference equals pi times our diameter of 12 feet the circumference equals 12 pi feet and that's our answer in terms of pi so that's one way to write it another way we can do this is to write our circumference in decimal form using an approximate value of pi since pi is irrational and we're going to use 3.14 so pi is approximately 3.14 so now i'll write out my formula circumference equals pi d then i'm going to plug in so i'm going to put circumference is approximately because we're using an approximate value of pi 3.14 times 12. so i plugged in my approximate value of pi and then our diameter of 12. now we can multiply to get an approximate circumference so circumference is approximately 37.68 feet so 37 and 68 hundredths feet is an approximate circumference for that circle with a diameter of 12 feet and again this is an approximate circumference since we used an approximate rounded version of pi so there you have it there's how you calculate the circumference of a circle given the radius or given the diameter we used the formulas pi d and 2 pi r depending on what we were given and we wrote our circumference in two different ways in terms of pi and then in decimal form using an approximate value of pi i hope that helped thanks so much for watching until next time peace