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Summary
DescriptionComparison of surface area vs volume of shapes.svg
English: Graphs of surface area A, against volume V, of all five Platonic solids and a sphere. It shows that the surface area decreases for rounder shapes (sphere being the lowest), and the surface-area-to-volume ratio decreases with increasing volume. The dashed blue lines show that when the volume of a randomly selected solid increases 8 (2³) times, its surface area increases 4 (2²) times. The dotted black line shows surface-area-to-volume ratio of 1.
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Short title
Graphs of surface area vs volume of the Platonic solids and a sphere
Image title
Graphs of surface area, A against volume, V of all 5 Platonic solids and a sphere by CMG Lee, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. The dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times. Shapes are from http://commons.wikimedia.org/wiki/File:Hamiltonian_platonic_graphs.svg .