Lesson 14Finding Cylinder Dimensions
Learning Goal
Let’s figure out the dimensions of cylinders.
Learning Targets
I can find missing information about a cylinder if I know its volume and some other information.
Lesson Terms
- cone
- cylinder
- sphere
Warm Up: A Cylinder of Unknown Height
Problem 1
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
Activity 1: What’s the Dimension?
Problem 1
The volume
The volume of this cylinder with radius 5 units is
cubic units. This statement is true: What does the height of this cylinder have to be? Explain how you know.
The volume of this cylinder with height 4 units is
cubic units. This statement is true: What does the radius of this cylinder have to be? Explain how you know.
Are you ready for more?
Problem 1
Suppose a cylinder has a volume of
What are some possibilities for the dimensions of the cylinder?
How many different cylinders can you find that have a volume of
cubic inches?
Activity 2: Cylinders with Unknown Dimensions
Problem 1
Each row of the table has information about a particular cylinder. Complete the table with the missing dimensions.
diameter (units) | radius (units) | area of the base (square units) | height (units) | volume (cubic units) |
---|---|---|---|---|
Lesson Summary
In an earlier lesson we learned that the volume,
We say that the volume depends on the radius and height, and if we know the radius and height, we can find the volume. It is also true that if we know the volume and one dimension (either radius or height), we can find the other dimension.
For example, imagine a cylinder that has a volume of
must be true. Looking at the structure of the equation, we can see that
Now imagine another cylinder that also has a volume of
must be true. Looking at the structure of this equation, we can see that