Explaining the relationship between diameter and circumference: ordered pairs
About this video
Mikey plotted diameter and circumference for three circular objects, such as (3, 9.5) and (5, 15.6). The points lie roughly on a line through zero, with circumference about 3.1-something times diameter, which is pi. The fourth object must keep that ratio, so (4, 12.6) is the choice.
You'll be able to
- recognize that diameter and circumference form a proportional relationship.
- check whether an ordered pair fits by multiplying the diameter by about 3.14.
- explain why real measurements may not give exactly pi.
Key words
- diameter
- The distance straight across a circle through its center.
- circumference
- The distance all the way around a circle.
- pi
- The special number, about 3.14159, that you get when you divide any circle's circumference by its diameter.
- ordered pair
- Two numbers (x, y) that give the position of a point; here (diameter, circumference).
Transcript
- [Instructor] We're told Mikey found the diameter and circumference for four circular objects. She plotted the measurements for three of the objects on the coordinate plane. All right, we see that here. Which ordered pair could represent Mikey's fourth object?
Pause this video, have a go at that. Okay, so these are circular objects, and on the horizontal axis, she plots diameter, and then we see circumference. So we can see this first object right over here, diameter of 3, circumference of 9.5. This one, diameter of 5, circumference of 15.6.
And what it looks like is that these all sit on a line. And not only do they sit on the line, but it looks like this line, if I were to eyeball it, it looks like it actually would go through zero. And of course, I am just eyeballing it. And so this at least looks like a proportional relationship, or roughly proportional relationship.
Remember, if you're taking real-world measurements of slightly imperfect objects in the real world, they might not all be perfectly circular. The measurements might get off a little bit, but this looks roughly proportional. And we can see that even here. If I start with, or if I have a diameter of 3, I am multiplying by, it looks like 3.1-something-something.
Once again, I'm multiplying here by 3.1-something-something. Here, also, it looks like I'm multiplying by 3.1-something-something. And those of you might already know, many of you might already know what that something-something is. The ratio between the circumference and the diameter of a circle is pi, which is just a fancy way of saying a special number that is 3.14159 and then keeps going on forever.
So essentially, another ordered pair is one where we see the same ratio between the diameter and the circumference. So if I take 4 and if I multiply it by 3.1-something-something, that indeed does get you pretty close to 12.6. So I like this choice. Here, 7 times 3-point-something would be between 21 and 22, not 30, so I don't like that.
6 times 3-point-something-something would be over 18, not 15, so I don't like that. 4 times 3-point-something-something would be over 12, so I'll rule that one out as well. So I like Choice A.
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