To calculate the surface area of the hat, we first need to find the radius of the base of the cone. The diameter is given as 38 cm, so the radius is half of that: 38 cm / 2 = 19 cm.
Next, we can use the slant height and radius to find the lateral surface area of the cone by using the formula:
Lateral surface area = π * radius * slant height.
Plugging in the values:
Lateral surface area = 3.14 * 19 cm * 30 cm = 1,789.8 square centimeters.
Therefore, the surface area of the hat is 1,789.8 square centimeters.
The correct answer is:
1,789.8 square centimeters