The radius of the base of a cone is 3 in . The height of the cone is 18 in . Find the exact volume of the cone. \( \mathrm{in}^{3} \)

To find the exact volume of the cone, you can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] In this case, the radius \( r = 3 \) inches and the height \( h = 18 \) inches. Plugging in the values: \[ V = \frac{1}{3} \pi (3^2)(18) = \frac{1}{3} \pi (9)(18) = \frac{1}{3} \pi (162) = 54\pi \] So, the exact volume of the cone is \[ 54\pi \, \text{in}^3 \] or approximately 169.65 in³ when calculated. Did you know that cones appear in various aspects of life, from the ice cream cone that brings joy on a summer day to architectural designs in modern buildings? This geometric shape is not just for math class, but also an inspiration in art and engineering! If you're working with volume problems, a common mistake people make is confusing the formulas for different shapes. Always double-check that you're using the right formula and that your measurements are in the same units before plugging them in—this will save you a lot of headache!