When viewed head-on, a cone appears to be a 2-dimensional, right-angle triangle. However, the large end of the cone, the base, is a full circle relative to the height. A cone is simply many circles with decreasingly smaller perimeters stacked on top of each other. The circles continue to get smaller until a point, the apex, forms. A cone is characterized as conical. The 3-D cone is stable in its ability to stand erect on its flat base. For example, bright orange cones indicate construction zones on freeways.
The volume of a cone is one-third the volume of a cylinder. The equation for volume (V) of a cone where pi equals 3.14, r equals the radius and h equals the height is V = pi x r^2 x (h/3). R^2 squares the radius, multiplying it by itself twice. The equation reads volume equals pi multiplied by the radius squared multiplied by the one-third the height. Always divide the height by three before multiplying it into the rest of the equation per the order of operations.
The surface area is the total area on the exterior of the cone, including the curved side and base. If you had to completely cover the cone in wrapping paper, for example, this is the amount you need. The equation for surface area (SA) where pi equals 3.14, r equals radius and s equals side length is SA = pi x r x s. If you do not know the side length, use the radius and height (the distance from the center of the base to the apex). Solve for side length by adding together the radius squared and height squared before taking the square root. The equation is SA = pi x r x sqrt((r^2)+(h^2)). Remember to solve for r squared and h squared before adding them together and solving for the square root.
Cones allow for stability and manageable transport. Cones are often seen in high-activity areas, such as freeways, athletic courts and playgrounds. The surface area of its base provides a large point of contact with the ground while the decrease in volume, due its apex, creates a shape that is hard to make unstable. Having an area that is one-third that of a cylinder decreases the potential for that volume to move and tip. The apex also allows the person to pick up the shape with one hand (if the object is light enough) to relocate. Apply the same concept to ice cream cones and birthday hats. A top hat is harder to stabilize than a birthday hat due to the larger volume and surface area. Ice cream cones are easier to hold than large bowls.