a. The side area of the hat is 484π cm².
b. The total area of the hat is 628π cm².
c. The volume of the hat is 3823.33 cm³.
To calculate the side area of the hat, we need the slant height. Using the Pythagorean Theorem, we can calculate the slant height to be:
s = √(r² + h²) = √(22² + 25²) = √484 = 22 cm
Therefore, the side area of the hat is:
πrs = 22π * 22 = 484π cm²
To calculate the total area of the hat, we need to add the area of the base to the side area. The area of the base is simply πr². Therefore, the total area of the hat is:
πrs + πr² = 484π + 22²π = 628π cm²
To calculate the volume of the hat, we use the following formula:
V = ⅓πr²h = ⅓π * 22² * 25 = 3823.33 cm³