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# 12.1: Surface Area of Cylinders

Difficulty Level: At Grade Created by: CK-12

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 Y=\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 H\begin{align*}H\end{align*} is dragged?

2. What changes occur to the net when the point R\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 R\begin{align*}R\end{align*} to confirm your conjecture.

## Problem 2 – Surface Area

6. Record these measurements:

Circle Area: __________

Rectangle L\begin{align*}L\end{align*}: __________

Rectangle Area: __________

Rectangle H\begin{align*}H\end{align*}: __________

7. Record the steps you performed to find the surface area of the cylinder:

1. _________________________________
2. _________________________________

8. What is the surface area of your cylinder?

9. How is the method used in #7 above related to the formula SA=2πR2+2πRH\begin{align*}SA = 2\pi R^2 + 2\pi RH\end{align*}?

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