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Investigating Curved Surface Area of a Cone

Author:paul venter, Anthony OR 柯志明, olivia.korum, Stephen Jull, Radha Devi
Topic:Area, Cone, Surface

Instructions:

  • Begin by familiarizing yourself with the GeoGebra tool. Identify the radius, height, and slant height of the cone.
  • Click and drag the red point to change the radius of the cone.
  • Observe how the cone’s shape changes when you manipulate the red point.

Task 1

Task 2: Exploring the Formula for Surface Area of a Cone

Surface Area Formula: Surface Area= r2 + rl where:
  • r is the radius of the base,
  • l is the slant height.

Guiding Questions:

  1. What happens to the surface area as you increase or decrease the radius r?

2. How does the slant height l change when you manipulate the cone?

3. What effect does this have on the lateral surface area?

Task 3: Calculating the Surface Area

Instructions:
  • Measure and record the radius r and slant height l of the cone at different points by manipulating the red point.

Calculate the surface area using the formula provided above.

Task 4: Understanding Lateral Surface Area

  • Visualisation in GeoGebra:
    • Use GeoGebra to explore how the slant height affects the lateral surface area.

Guiding Questions:

  1. How does changing the slant height affect the overall surface area of the cone?
  2. Can you describe a real-life scenario where understanding the surface area of a cone would be important?

Task 5: Challenge Task

Extension Activity:

  • Consider how the surface area of the cone changes if you increase the slant height but keep the radius constant. How would you expect the surface area to change if you double the radius?

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