FACTOID # 6: Michigan is ranked 22nd in land area, but since 41.27% of the state is composed of water, it jumps to 11th place in total area.

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Encyclopedia > Prolate spheroid

A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball). If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth).

 Prolate spheroid. Oblate spheroid.

The sphere is a special case of the spheroid in which the generating ellipse is a circle.

A spheroid is a special case of an ellipsoid where two of the three major axes are equal.

## Volume

Prolate spheroid:

• volume is

Oblate spheroid:

• volume is

where

• a is the major axis length
• b is the minor axis length

## Surface area

A prolate spheroid has surface area

An oblate spheroid has surface area

b(b + aˇarcsin(e)/e).

Here e is the eccentricity of the ellipse, defined as

Results from FactBites:

 Stent delivery catheter with enhanced balloon shape - Patent 6221043 (5381 words) Immediately proximal to the central segment of the balloon is a proximal segment of the balloon in the form of a prolate spheroid having a distal end that is the same diameter as the diameter of the cylindrical central segment and a proximal end that has a slightly reduced diameter. The central prolate spheroid segment 25 is joined at its proximal end to a first conical segment 24B which is joined to a second conical segment 24A that is joined to a cylindrical segment 23 that is fixedly attached to the outer shaft 50 of the balloon angioplasty catheter 20. The central prolate spheroid segment 25 is joined at its distal end to a first conical segment 28B that is joined to a second conical segment 28A that is joined to a cylindrical segment 29 that is fixedly attached to the distal end of the inner shaft 40.
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