MENSURATION · CONE · INVESTIGATION 10
Cone & Slant Height Explorer
Investigate the relationship between radius, height, slant height, curved surface area and volume of a cone.
Interactive mathematical workspace
Live simulationThe model updates as you adjust the apparatus controls. Values are simulated mathematical outputs, not physical measurements.
Primary result—
Secondary result—
Relationship—
Check—
Adjust a control to begin the investigation.
Learning objective
To investigate Cone & Slant Height Explorer using a dynamic mathematical model and justify a conclusion from recorded values.
Mathematical principle
l = √(r²+h²) · CSA = πrl · V = ⅓πr²h
Procedure
1
Enter student details and note the initial settings.
2
Change one independent variable while keeping the others fixed.
3
Observe the visual model and note the calculated values.
4
Repeat with at least three different settings and record the readings.
5
Use the pattern in your observations to write a mathematical conclusion.
Variables
Independent: the control being changed. Dependent: calculated result. Controlled: other settings held constant.
Guided investigation: Change r and h and compare slant height, curved area and volume.
Common errors to avoid
- Changing several variables simultaneously.
- Recording rounded values before completing calculations.
- Confusing linear, square and cubic units.
- Writing a conclusion that is not supported by observations.
Live mathematical analysis
l = √(r²+h²) · CSA = πrl · V = ⅓πr²h
The working will appear here.
Observation table
| Trial | Settings | Result 1 | Result 2 |
|---|---|---|---|
| Run and record trials to populate this table. | |||
Compare the readings and identify the pattern.
Digital practical notebook
Recorded trials
| # | Settings | Result 1 | Result 2 | Time |
|---|
Knowledge check
Select the best answer. Feedback is provided after checking.
Assessment score0 / 5
Investigation challenge
For r = 3 cm and h = 4 cm, calculate l.