Lesson 12Filling 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.

  1. A cone
  2. A sphere
  3. A cylinder
  4. A rectangular prism

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.

  1. Before you get started, make a prediction about the shape of the graph.

    1. Check Reset and set the radius and height of the graduated cylinder to values you choose.

    2. Let the cylinder fill with different amounts of water and record the data in the table.

    open applet in presentation mode

  3. Create a graph that shows the height of the water in the cylinder as a function of the water volume.

    A blank coordinate plane.

  4. Choose a point on the graph and explain its meaning in the context of the situation.

    open applet in presentation mode
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.

  1. Before you get started, make a prediction about the shape of the graph.

  2. Fill the cylinder with different amounts of water and record the data in the table.

    volume (ml)

    height (cm)

  3. Create a graph that shows the height of the water in the cylinder as a function of the water volume.

    A blank coordinate plane.

  4. 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.

Coordinate plane, horizontal, volume in milliliters, 0 to 100 by tens, vertical, height in centimeters, 0 to 14 by twos. Line segments from origin to 40 comma 9, then on to 100 comma 12.

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.

A graph of volume in millimeters vs height in centimeters. There are 3 segments. Graph starts at (0,0) and goes up with differing steepness

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.

A graph of volume (ml) vs height (cm). Graph starts at (0,0) and curves upward and flattens out

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, and , with the same height, but has a radius of 3 cm and has a radius of 6 cm.

A cylinder, D with a radius of 3 cm and a cylinder, E with a radius of 6 cm. The heights are both h.

If we pour water into both cylinders at the same rate, the height of water in will increase faster than the height of water in due to its smaller radius. This means that if we made graphs of the height of water as a function of the volume of water for each cylinder, we would have two lines and the slope of the line for cylinder would be greater than the slope of the line for cylinder .