Surface Area
Geometry
Level
2
For a fixed volume, which of these shapes has the smallest surface area?
Ellipsoid
Sphere
Oblate Spheroid
Cone
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Consider a sphere of fixed volume. Without changing its volume, you can "morph" it into any of the other shapes listed by stretching one side and flattening another, or bending the sphere at one point and extending it at another, as a couple of examples. In doing so, the surface area is necessarily increased for all other shapes considered. Since the volume remains constant, the shape with the least surface area is the sphere.