Volume and surface area help us measure the size of 3D objects. We’ll start with the volume and surface area of rectangular prisms. From there, we’ll tackle trickier objects, such as cones and spheres.
It's pretty difficult to work, mentally, with 3D objects. One way of overcoming that difficulty is in thinking about cross sections of such objects. These are 2D slices of 3D objects, and so we're back with the familiar 2D world.
Named after Helge von Koch, the Koch snowflake is one of the first fractals to be discovered. It is created by adding smaller and smaller equilateral bumps to an existing equilateral triangle. Quite amazingly, it produces a figure of infinite perimeter and finite area!