A cylinder is a 3-dimensional figure with two congruent circles as bases that are parallel to each other with the same size shape from the bottom to top. Below is an example of a cross-section of a cylinder. All cross-sections are congruent circles that are parallel to the bases of the cylinder.

Click on the image below to view the net of a cylinder. Click the orange center of the circle to “unroll” the cylinder.

The net of a cylinder is a rectangle and two circles, as shown below, and observed when the cylinder was unrolled.

The circular top and bottom, or bases, of the cylinder have the same diameter as the cylinder.

Pause and Reflect: What shape is the lateral surface of a cylinder? What are the dimensions of this lateral surface in terms of the radius, r, of the cylinder, and the height, h, of the cylinder?

Interactive popup. Assistance may be required. Possible Response

The lateral surface of a cylinder is a rectangle!

The width of the rectangle is equal to the circumference of the cylinder, which is 2πr.

The length of the rectangle is the height of the cylinder, h.

Answer the following questions.

• The height of the cylinder is the same as the height of the rectangle that forms the curved lateral surface of the cylinder. The length of the rectangle is the same as the ___?___ of the cylinder.
  
  Interactive popup. Assistance may be required. Check Your Answer circumference
  
  
• Think about the paper wrapper on a soup can… when you cut it off the can, it is a rectangle that is the height of the can and is long enough to fit around the circumference of the circular top and bottom of the soup can. The length of the rectangle is the circumference of the cylinder because the outside “wrapper” of the cylinder has to be long enough to fit exactly around ___?___.
  
  Interactive popup. Assistance may be required. Check Your Answer the outside of the cylinder
  
  
• The total surface area of the cylinder includes two ___?____ Interactive popup. Assistance may be required. Check Your Answer circles
  that have the same radius and diameter as the cylinder and one ___?____ Interactive popup. Assistance may be required. Check Your Answer rectangle
  whose height is _______?_______ Interactive popup. Assistance may be required. Check Your Answer the same as the cylinder's height
  and whose length is the ____?____of the cylinder. Interactive popup. Assistance may be required. Check Your Answer circumference

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