00:02: Let's review the idea of the circumference of the circle and how to find it. Remember that the circumference of a circle is the distance around the circle. It's kind of like the idea of perimeter when you're dealing with polygons like rectangles and hexagons, but of course there are no angles and there are no straight line segments. 00:24: Now, if you remember the special number pie which we often just represent with 3.14, pi is a ratio. It's a very special ratio. It's the ratio of the circumference of a circle to its diameter. So remember that a diameter is a chord which is a line segment that passes through the center of the circle. So pi is actually defined to be the total length around the circle, the circumference divided by the diameter. Now, from that little definition, if we just imagine multiplying both sides by D, we can see that the circumference is equal to D times pi or pi times the diameter. 01:18: Now, in a lot of applied situations, you don't have the diameter, but rather the radius And of course remember, the radius is just half of the diameter. It's this length from the center of the circle out to the circle itself. And I'm just gonna go ahead and label that R. So the radius is just half of the diameter. So another formula that we use when we're finding the circumference is circumference equals 2 pi R. And what we've done there is we've multiplied pi by the radius, but that we've had to double it because the radius is only half of a full diameter of the circle. 01:58: So let's take a specific case where we have a circle and we're given that its radius is 3 centimeters. That if we wanted to find the circumference, we would use the formula 2 pi R. And so we'd have 2 times pi times the radius which is 3. And if we multiply those together and just keeping the pi as itself so that we have the exact value, we end up with 6 pi and then that would be centimeters. And if you want to get a numerical decimal approximation, you can use 3.14 or whatever approximation you're told to use and then just multiply that way and you would end up getting 18.84 centimeters.
What is the radius of the circle in the example?
Responses
A 3 cm3 cm
B 5 cm5 cm
C 7 cm
A. 3 cm
What is the circumference of the circle in the example?
Responses
A 2π2π
B 4π4π
C 6π