Unit 5, Lesson 11
Filling Containers
Grade 8
11.1
Warm-up
Which Three Go Together: Solids
Which three go together? Why do they go together?
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Which three go together? Why do they go together?
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.
| volume (ml) | ||||||
|---|---|---|---|---|---|---|
| height (cm) |
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.
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.
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, D and E, with the same height, but D has a radius of 3 cm, and E has a radius of 6 cm.
If we pour water into both cylinders at the same rate, the height of water in D will increase faster than the height of water in E because of 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 D would be greater than the slope of the line for Cylinder E.