File:Comparison of surface area vs volume of shapes.svg
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Captions
Captions
Graphs of surface area A, against volume V of all the 5 Platonic solids as well as of a sphere
Summary
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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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| Date | (UTC) | |
| Source |
Own work
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| Author | cmglee |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:41, 26 August 2021 | | 512 × 512 (23 KB) | Cmglee (talk | contribs) | Use own shapes from http://commons.wikimedia.org/wiki/File:Hamiltonian_platonic_graphs.svg |
| 00:35, 21 November 2019 |  | 512 × 512 (27 KB) | Cmglee (talk | contribs) | Note increasing volume 8 times increases area 4 times. | |
| 19:20, 14 June 2013 |  | 512 × 512 (26 KB) | Cmglee (talk | contribs) | {{Information |Description={{en|Graphs of surface area against volume of all 5 Platonic solids and a sphere, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume.}} |Date=2013... |
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