This video continues with the Menger Sponge, specifically looking at how to calculate its volume.
The fractal is created by starting with a cube, dividing the cube into 27 equally sized smaller cubes, and removing the middle cube on each of the 6 faces as well as the cube from the center, leaving 20 of the original 27 cubes. This process is then repeated for each of the remaining 20 cubes and so on.
When this process is carried out infinitely manner times, the Menger Sponge is created. This fractal has dimension approximately equal to 2.73 and has infinite surface area but the volume is equal to zero.
EulersAcademy.org
