This activity is intended to supplement Geometry, Chapter 11, Lesson 2.
Time required: 30 minutes
Students will explore a net representation for a right cylinder. The surface area will be developed from the parts of the net.
Topic: 3-Dimensional Geometry
Construct 3- dimensional prisms and pyramids from nets.
Calculate the surface area of a right prism or cylinder.
Teacher Preparation and Notes
This activity is designed to be used in a high school or middle school geometry classroom.
This activity is designed to be student-centered.
The surface area of a right cylinder with base radius =R and height =H is SA=2πR2+2πRH. The activity asks students to notice that the circumference of the circle is the length of the rectangle in the net.
The points R and H control the radius and the height of the cylinder. When R is dragged, the length of the rectangle also changes (because the length = circumference of the circle). The height of the rectangle does not change when R is dragged.
Note: Measurements can display 0, 1, or 2 decimal digits. If 0 digits are displayed, the value shown will round from the actual value. To change the number of digits displayed:
Move the cursor over the value so it is highlighted.
Press + to display additional decimal digits or - to decrease digits.
Problem 1 – Nets
A net is a pattern that can be cut out and folded into a 3-dimensional figure. Students should see a partial net of a right cylinder. If the rectangle of the net were rolled up, the circle would be the top face of the cylinder (like a lid of a jar).
Note: Display measurements with 2 decimal digits. To do this, hover the cursor over the measurement and then press the plus key (+).
Next, they should use the Calculate tool to divide the length of the rectangle by the radius of the circle to find that the width of the rectangle is the same as the circumference of the circle.
Problem 2 – Surface Area
Press the ENTER button to start and end the text.