Volume Voyage Slides
VOLUME BLUEPRINT
Tier 2 Intervention: 3D Solids
Today's Mission
Connect
Discover how cylinders, cones, and spheres are related.
Calculate
Use step-by-step blueprints to find the total volume.
Measure
Practice with real-world objects in our workshop.
Standard: CO 8.G.C.9
"I can solve volume problems for cylinders, cones, and spheres."
The 3:1 Connection
FULL
Cylinder
Base Area × Height
\( V = \pi r^2 h \)
1
2
3
3 Cones
Same height & radius!
\( V_{cone} = \frac{1}{3} V_{cylinder} \)
Think: If the cylinder holds 30 cups of water, how much does the cone hold?
The Calculation Blueprint
1
Identify the Radius (r) and Height (h).
2
Square the radius: r × r
3
Multiply by \(\pi\) (use 3.14) and height (\(h\)).
4
For a cone? Divide by 3 at the end!
The Sphere Formula
Bonus Master Level
A sphere is like 4 cones put together (but with a catch!)
Formula:
\[ V = \frac{4}{3} \pi r^3 \]
Be careful! Use \(r^3\) which is r × r × r.
Workshop Lab: Soup Can
Item: Tomato Soup Type: Cylinder
Your Task:
- 1 Measure the Diameter and divide by 2.
- 2 Measure the Height.
- 3 Apply the Blueprint Formula!
Ready to Measure? Grab your rulers!
Volume Blueprint Worksheet
Volume Blueprint
Tier 2 Intervention Workshop
Name:
Date:
Part 1: The 3:1 Connection
If a cylinder and a cone have the same radius and the same height, how many cones of water fill the cylinder?
Cylinder
Full
1
2
3
Fill in the blanks:
It takes cones to fill 1 cylinder.
This means a cone is exactly / the size of a cylinder!
Part 2: Calculation Blueprints
CYLINDER BLUEPRINT \( V = \pi r^2 h \)
Radius
Multiply by itself
\( r^2 \)
Height
Total Volume:
\( V = \)
CONE BLUEPRINT \( V = \frac{1}{3} \pi r^2 h \)
Follow Cylinder Steps...
Copy cylinder result here first.
DIVIDE BY 3
Total Volume:
\( V = \)
Part 3: Real Object Workshop
Use your ruler to measure the real objects at your station. Round measurements to the nearest whole number.
| Object | Shape | Radius (\(r\)) | Height (\(h\)) | Work Area & Result |
|---|
| Soup Can | Cylinder | | | |
| Party Hat | Cone | | | |
| Tennis Ball | Sphere | | N/A | \( V = \frac{4}{3} \pi r^3 \) |
Part 4: Mastery Challenge
Problem 1
A cylindrical water tank has a radius of 5 meters and a height of 10 meters. How much water can it hold? (Use 3.14 for \(\pi\))
Answer:
Problem 2
An ice cream cone has the same radius (5 cm) and height (10 cm) as a small cylindrical cup. If the cup holds 750 cm³ of ice cream, how much does the cone hold? (Hint: Use the 3:1 connection!)
Answer:
Volume Exit Ticket
Exit Ticket
Volume Check
Standard 8.G.C.9
Name
Date
1
The Big Connection
If a cylinder holds 90 cubic inches of volume, how much would a cone with the same height and radius hold?
270
cu inches
45
cu inches
30
cu inches
Explain your choice: __________________________________________________________________
2
Apply the Blueprint
Find the volume of a cylinder with a radius of 2 cm and a height of 5 cm. (Use 3.14 for \(\pi\))
Show your work here
Volume =
cm³
How do you feel about today's lesson?
Confused
Getting there
I've got it!
Volume Progress Checklist
Volume Progress Tracker
Tier 2 Small Group Intervention
Standard: CO 8.G.C.9
Group Name
Session Date
Instructor
| Student Name | Identifies
r vs. d | Applies
\( r^2 \) correctly | 3:1 Cylinder/Cone
Conceptual | Uses Calculator
Accurately | Adds Proper
Units (u³) | Mastery
(0-3) |
| --- | --- | --- | --- | --- | --- | --- |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
Mastery Key
- 3 Mastered (Independent)
- 2 Progressing (Guided)
- 1 Emerging (Heavy Support)
- 0 No evidence
Misconception Alert
Watch for students multiplying the diameter instead of the radius. Remind them: "Radius is half of the circle!"
Anecdotal Notes
