Unfolding Cylinders
Unfold and fold a net for a cylinder. Change the dimensions of the cylinder to explore its geometry.
Imagine you are going to cut a cylinder along one side and unfold it into a flat shape.
- What shapes do you predict you will see when the cylinder is completely unfolded?
- Predict what will happen to the rectangle if the radius of the cylinder increases but its height stays the same.
- Explain your reasoning before moving the slider.
Respond below:
Were your predictions correct? Explain what you noticed.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
What shapes do you need to form the net of a cylinder?
What can change in the net of a cylinder?
The only two unknowns you need for surface area of a cylinder is height and diameter (or radius).
Fill in the blank The circles must be the same __________. The rectangle's height matches the cylinder's __________. The rectangle's length matches the circle's __________. Hint: Think about what happens when the rectangle wraps all the way around the cylinder.
Use the length and height above to create an expression for area of the rectangle.
Create an expression for the area of the top and bottom circle.
Create an expression that adds the area of the rectangle and the area of both circles.
Enrichment
Which variable has a greater effect on increasing surface area, the radius or the height? Explain why you believe this to be true.