A party hat has a diameter of 18 centimeter and a height of 25 centimeter. Find the volume of air it can occupy. Volume \( = \)

To find the volume of the party hat, model it as a cone. The formula for the volume of a cone is \( V = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Given the diameter of 18 cm, the radius \( r \) is 9 cm. Now, substituting \( r = 9 \) cm and \( h = 25 \) cm, you get: \[ V = \frac{1}{3} \pi (9^2)(25) = \frac{1}{3} \pi (81)(25) = \frac{2025}{3} \pi \approx 675 \pi \text{ cm}^3 \] So, the party hat can occupy approximately \( 2110.62 \) cm³ of air, using \( \pi \approx 3.14 \). Did you know that the use of hats goes back thousands of years? Ancient Egyptians wore them to symbolize status, while in ancient Greece and Rome, hats were common fashion items that represented citizenship and social class. Today, hats are often worn for protection from the elements or as a fun way to express individuality, like these playful party hats! When making calculations involving cones, a common mistake is miscalculating the radius. Always remember that the radius is half of the diameter! Additionally, double-check that you’re plugging the radius into the formula correctly and paying attention to the units. This ensures you get the right volume without a hitch!