Whe formula for the volume of \( a \) cone is \( V=\frac{1}{3} \pi r^{2} h \) where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Did you know that the formula for the volume of a cone comes from its relationship to a cylinder? If you take a cylinder with the same base and height as the cone, the volume of the cylinder is \( V_{cylinder} = \pi r^2 h \). The cone, however, only takes up one-third of that volume, which is why we have the \( \frac{1}{3} \) factor in the formula! In real-world applications, knowing how to calculate the volume of a cone can come in handy for things like designing party hats, ice cream cones, or even in architecture when creating structures with a cone shape. Imagine wanting to know how much ice cream to order for a cone-shaped celebration; this formula will be your best friend in planning the perfect party!