Lesson 11Filling Containers
Learning Goal
Let’s fill containers with water.
Learning Targets
I can collect data about a function and represent it as a graph.
I can describe the graph of a function in words.
Lesson Terms
- cylinder
Warm Up: Which One Doesn’t Belong: Solids
Problem 1
These are drawings of three-dimensional objects. Which one doesn’t belong? Explain your reasoning.
Activity 1: Height and Volume
Problem 1
Use the applet to investigate the height of water in the cylinder as a function of the water volume.
Before you get started, make a prediction about the shape of the graph.
Check Reset and set the radius and height of the graduated cylinder to values you choose.
Let the cylinder fill with different amounts of water and record the data in the table.
Create a graph that shows the height of the water in the cylinder as a function of the water volume.
Choose a point on the graph and explain its meaning in the context of the situation.
Print Version
Your teacher will give you a graduated cylinder, water, and some other supplies. Your group will use these supplies to investigate the height of water in the cylinder as a function of the water volume.
Before you get started, make a prediction about the shape of the graph.
Fill the cylinder with different amounts of water and record the data in the table.
volume (ml)
height (cm)
Create a graph that shows the height of the water in the cylinder as a function of the water volume.
Choose a point on the graph and explain its meaning in the context of the situation.
Activity 2: What Is the Shape?
Problem 1
The graph shows the height vs. volume function of an unknown container. What shape could this container have? Explain how you know and draw a possible container.
Problem 2
The graph shows the height vs. volume function of a different unknown container. What shape could this container have? Explain how you know and draw a possible container.
Problem 3
How are the two containers similar? How are they different?
Are you ready for more?
Problem 1
The graph shows the height vs. volume function of an unknown container. What shape could this container have? Explain how you know and draw a possible container.
Lesson Summary
When filling a shape like a cylinder with water, we can see how the dimensions of the cylinder affect things like the changing height of the water. For example, let’s say we have two cylinders,
If we pour water into both cylinders at the same rate, the height of water in