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.

  1. Name a segment that is a radius. How long is it?
  2. 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.
(From Unit 5, Lesson 11.)

Problem 4

  1. 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.

    Blank grid, origin O. Horizontal axis, scale 0 to 7, by 1's. Vertical axis, scale 0 to 14, by 2's. 
  2. Based on the graph, can this be a proportional relationship? Why or why not?
(From Unit 5, Lesson 7.)