Lesson 12
Exploring Circumference
Let’s explore the circumference of circles.
Problem 1
Diego measured the diameter and circumference of several circular objects and recorded his measurements in the table.
object | diameter (cm) | circumference (cm) |
---|---|---|
half dollar coin | 3 | 10 |
flying disc | 23 | 28 |
jar lid | 8 | 25 |
flower pot | 15 | 48 |
One of his measurements is inaccurate. Which measurement is it? Explain how you know.
Problem 2
Complete the table. Use one of the approximate values for \(\pi\) discussed in class (for example 3.14, \(\frac{22}{7}\), 3.1416). Explain or show your reasoning.
object | diameter | circumference |
---|---|---|
hula hoop | 35 in | |
circular pond | 556 ft | |
magnifying glass | 5.2 cm | |
car tire | 71.6 in |
Problem 3
\(A\) is the center of the circle, and the length of \(CD\) is 15 centimeters.
- Name a segment that is a radius. How long is it?
- Name a segment that is a diameter. How long is it?
![A circle with center point A. Diameter CD, 15 cm. Points on the circle are C, E, G, B, D.](https://staging-cms-im.s3.amazonaws.com/XZFdo8Xegbwd8idriKFxdh2F?response-content-disposition=inline%3B%20filename%3D%227.3.PP.New.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%277.3.PP.New.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T181844Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=84c0166a5461b25fd2b71d64c5968509f1a6b5b2cfe61e5908953cf91cc9110c)
Problem 4
-
Consider the equation \(y=1.5x +2\). Find four pairs of \(x\) and \(y\) values that make the equation true. Plot the points \((x, y)\) on the coordinate plane.
- Based on the graph, can this be a proportional relationship? Why or why not?