Nanotechnology provides new ways to make novel materials. Surface area is a key feature of devices that utilize chemical reactions. Mathematics gives us a way to analyze the surface to volume ratio.
Watch this video to see how the same amount of material can be processed to create an extremely high surface area. This is useful for constructing high capacity battery electrodes.
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Photograph by Alexander Kozen, ANSLab University of Maryland
See if you can create a spreadsheet that models the effect of decreasing particle size on surface to volume ratio for a bulk material. (hint: calculate the surface area for different diameter spheres or size cubes and then figure out what happens as the diameter decreases while keeping the total volume the same. )
v= 4/3 Π r 3
sa= 4 Πr2