Here's how to calculate the amount of cork needed for each circular slate table mat:

1. Calculate the area of the table mat:

We know the diameter is 22 cm. To find the area, we need the radius, which is half the diameter: radius = diameter / 2 = 22 cm / 2 = 11 cm
Area of a circle = * radius^2
Area of the table mat = * 11 cm^2 380.13 cm^2
2. Determine the area of the cork covering:

Since the cork only covers the bottom, we don't need to consider the curved edge of the table mat.
Therefore, the area of the cork covering is equal to the area of the circle calculated above.
3. Amount of cork needed:

We need to know the thickness of the cork to determine the final volume needed. Let's say the cork is 5 mm thick (0.5 cm).
Volume of cork = area of cork covering * thickness
Volume of cork = 380.13 cm^2 * 0.5 cm 190.06 cm^3
Therefore, approximately 190.06 cubic centimeters of cork are needed for each circular slate table mat.