Lesson 3

Exploring Circumference

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.

Solution

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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

Solution

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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?

Solution

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(From Unit 3, Lesson 2.)

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.

2. Based on the graph, can this be a proportional relationship? Why or why not?

Solution

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(From Unit 2, Lesson 10.)