Net of a Cylinder
Net of a Cylinder is a Grade 8 geometry skill in Saxon Math Course 3, Chapter 6, where students learn that unfolding a cylinder produces a net consisting of two circles (the bases) and one rectangle (the lateral surface). Understanding the cylinder net enables accurate surface area calculations and connects 3D geometry to 2D measurement.
Key Concepts
Property A cylinder has two circular bases and a lateral surface that unwraps to form a rectangle. The surface area is given by the formula $S = 2\pi rh + 2\pi r^2$.
Examples A cylinder's net is a rectangle with two identical circles attached to its shorter, opposite sides. In the formula $S = 2\pi rh + 2\pi r^2$, the $2\pi rh$ part calculates the area of the rectangular label. The $2\pi r^2$ part of the formula represents the combined area of the two circular lids on the top and bottom.
Explanation A can of soup is a perfect cylinder. If you were to peel off its label, the label would become a flat rectangle. The top and bottom lids of the can are just two circles. So, a cylinder's net is simply one rectangle with two circles attached, one at the top and one at the bottom.
Common Questions
What does the net of a cylinder look like?
The net of a cylinder has three parts: two congruent circles for the top and bottom bases, and one rectangle whose width equals the height of the cylinder and whose length equals the circumference of the base.
How do you use the net of a cylinder to find surface area?
Find the area of both circular bases using pi r squared and the area of the rectangle using height times circumference (2 pi r times h), then add all three together.
Why does the rectangle in the net have a length equal to the circumference?
When you unroll the curved lateral surface of a cylinder, it forms a flat rectangle. Its length equals the circumference of the circular base because the lateral surface wraps exactly once around the circle.
How is the net of a cylinder different from the net of a prism?
A cylinder net has circular bases and a rectangular lateral surface. A prism net has polygonal bases (like rectangles or triangles) and rectangular lateral faces.
Where is net of a cylinder taught in Grade 8?
Net of a cylinder is covered in Saxon Math Course 3, Chapter 6: Number and Operations and Data Analysis and Probability.