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Net of a Cone

The following applet can be used to explore the net of a Cone and it's surface area formula.

Instructions:

  1. Use slide r to change the radius of the base and slider h to change height of the cone.  Finally use the Net slider or press the play button to show how the cone unraps into its net.

Questions:

1)  What shape is the base of the cone?

2)  What shape is the lateral surface of the cone?

3)  What are the radii of the 2 shapes in terms of r, h and slant height?

4)  What is the relationship between the circumference of the base and the arc length of the lateral surface?

5)  What are the formulas for arc length and area of the lateral surface in term of the slant height?

6)  What is the formula for arc length of the lateral surface in term of r?

7)  What is the formula for arc length of the lateral surface in term of r and slant height?

8)  Using the answers to questions 4, 5, and 6 can you derive the formula found on our reference sheet for surface area of a cone?  

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