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18 January, 11:14

What structure encloses the most space with the least surface area (has the the highest volume to surface area ratio) ?

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  1. 18 January, 11:29
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    That structure would be the Sphere.

    With a Volume of V = 4/3*π*r**3

    And a surface area of A = 4*π*r**2

    r = (A / (4*π)) * * 1/2

    V = 4/3*π * [A^ (3/2) / (8 π^ (3/2)) ] = A^ (3/2) / (6 sqrt (π))

    We can graph V in tems of A

    And compare it to the graph y = x

    We can see that the Volume increases more rapidly compared to the Area
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