Computes the volume, V, and area, A,
of an oblate spheroid (with vertical axis of symmetry) with
"equatorial radius" a (in the horizontal plane) and
"polar radius" c (vertical), c ≤ a.
The calculation is from its "bottom pole",
z = 0, to a given height,
z = H
(so 0 ≤ H ≤ 2 c).
A spheroid is an ellipsoid of revolution; and oblate
if flattened, i.e., c ≤ a (a sphere if equal).
As 0→c→a, it is
2πa²→A→4πa²
(the latter, say, As being the area of a sphere,
when c = a).
† If c ≮ a,
the final, analytical area cannot be calculated.
Curves are drawn for V(z) and
A* = A(z)⁄As
(thus not exceeding 1),
z ∈ (0, 2c), with z the distance
from the bottom pole.
Other suggested data: a = 6 (for eccentricity);
a, c, h = 3.31, 2.2, 2.2 (for V ≅ 50). |
• Weisstein, Eric W.
"Solid of
revolution". From MathWorld—a Wolfram web resource.
vol ← a √[1 − (z⁄c)²]
• Weisstein, Eric W.
("Ellipsoid of
revolution"). From MathWorld—a Wolfram web resource.
area ← a √(1 + Ecc²z²)
• Wood, Alan, "Alan Wood's
Unicode
Resources".
• 1881-10-11: Richardson, Lewis Fry
(1953-09-30). |
