12.1: Surface Area of Cylinders
This activity is intended to supplement Geometry, Chapter 11, Lesson 2.
Problem 1 – Nets
Start the Cabri Jr. application by pressing the APPS key and selecting CabriJr. Open the file CYLINDER by pressing \begin{align*}Y=\end{align*}, selecting Open..., and selecting the file. You should see a partial net of a right cylinder.
1. What changes occur to the net when the point \begin{align*}H\end{align*} is dragged?
2. What changes occur to the net when the point \begin{align*}R\end{align*} is dragged?
3. Record 2 sets of measurements of the net:
Circle Radius | Rectangle Height | Rectangle Length |
---|
4. What is the result when you divide the Rectangle Length by the Circle Radius?
5. Explain this result. Drag point \begin{align*}R\end{align*} to confirm your conjecture.
Problem 2 – Surface Area
6. Record these measurements:
Circle Radius: __________
Circle Area: __________
Rectangle \begin{align*}L\end{align*}: __________
Rectangle Area: __________
Rectangle \begin{align*}H\end{align*}: __________
7. Record the steps you performed to find the surface area of the cylinder:
- _________________________________
- _________________________________
8. What is the surface area of your cylinder?
9. How is the method used in #7 above related to the formula \begin{align*}SA = 2\pi R^2 + 2\pi RH\end{align*}?
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