Nets (Leaving Cert Mathematics): Revision Notes

Net of a Cylinder

What is a Net?

A net is a 2D layout of a 3D object that can be folded to recreate the 3D shape. For a cylinder, the net includes:

1. Two Circles: Represent the top and bottom faces (bases) of the cylinder.
2. One Rectangle: Represents the curved surface of the cylinder when laid flat.

Geometry of the Net of a Cylinder

Circles:

Each has a radius $r$

• The area of each circle is $\pi r^2$

Rectangle:

• Width = height of the cylinder ($h$).
• Length = circumference of the circular base ($2\pi r$).
• Area of the rectangle is $2\pi r h$

Surface Area of a Cylinder

The total surface area of a cylinder is the sum of the areas of the two circles and the rectangle:

$$\text{Surface Area} = 2\pi r^2 + 2\pi r h$$

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Worked Example

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Summary

• Net of a Cylinder: Consists of two circles (top and bottom) and one rectangle (curved surface).
• Surface Area Formula: $\text{Surface Area} = 2\pi r^2 + 2\pi r h$
• Practice drawing nets and calculating areas to enhance understanding of cylinders in geometry.