A nón lá is a traditional Vietnamese hat in the shape of a perfect cone. What is the surface area of a hat with a diameter of 38 cm and a slant height of 30 cm? Use 3.14 for pi.
The radius of the base of the hat is half of the diameter, so it is 38 cm / 2 = <<38/2=19>>19 cm.
The slant height represents the slanted side of the cone, which can be considered a slanted height of a right triangle with a height of 30 cm and a hypotenuse of 19 cm.
Using the Pythagorean theorem, we can find the height of the triangle:
h² = c² - a²
h² = 19² - 30²
h² = 361 - 900
h² = -539
There are no real solutions for this equation, so it is not possible to have a slant height of 30 cm with a diameter of 38 cm.