Lesson 16Finding Cone Dimensions
Learning Goal
Let’s figure out the dimensions of cones.
Learning Targets
I can find missing information of about a cone if I know its volume and some other information.
Lesson Terms
- cone
- cylinder
- sphere
Warm Up: Number Talk: Thirds
Problem 1
For each equation, decide what value, if any, would make it true.
Activity 1: An Unknown Radius
Problem 1
The volume
The volume of this cone with height 3 units and radius
Activity 2: Cones with Unknown Dimensions
Problem 1
Each row of the table has some information about a particular cone. Complete the table with the missing dimensions.
diameter (units) | radius (units) | area of the base (square units) | height (units) | volume of cone (cubic units) |
---|---|---|---|---|
Are you ready for more?
Problem 1
A frustum is the result of taking a cone and slicing off a smaller cone using a cut parallel to the base.
Find a formula for the volume of a frustum, including deciding which quantities you are going to include in your formula.
Activity 3: Popcorn Deals
Problem 1
A movie theater offers two containers:
Which container is the better value? Use 3.14 as an approximation for
Lesson Summary
As we saw with cylinders, the volume
If we know the radius and height, we can find the volume. If we know the volume and one of the dimensions (either radius or height), we can find the other dimension.
For example, imagine a cone with a volume of
Looking at the structure of the equation, we can see that
Now imagine a different cone with a volume of
so the height must be 6 cm. Can you see why?