Ellipsoid Volume Calculator
Calculate the volume of an ellipsoid using three semi-axis lengths with ellipsoid volume calculator. Get results with the ellipsoid volume formula and steps.
π setting: π = 3.14159265
π Precision:
cm
cm
Ellipsoid Volume
251.3274cm³
Decimals:
Step-by-Step Mathematical Solution
Formula:V = (4/3) × π × a × b × c
Steps:
1.Semi-axes: a = 3 cm, b = 4 cm, c = 5 cm
2.Formula: V = (4/3) × π × a × b × c
3.Multiply axes: a × b × c = 3 × 4 × 5 = 60
4.Multiply by (4/3)π ≈ 4.1887902: V ≈ 251.3274 cm³
Calculated Volume:251.3274 cm³
What Is a Ellipsoid?
An ellipsoid is a three-dimensional surface that is the 3D analogue of an ellipse. Spheres, eggs, rugby balls, and planets are ellipsoidal.
Volume of a Ellipsoid Formula
Standard Formula
V = (4/3) × π × a × b × c
Formula Variables Explained:
aSemi-axis a
Radius along the x-axis.
bSemi-axis b
Radius along the y-axis.
cSemi-axis c
Radius along the z-axis.
The formula for ellipsoid volume is V = (4/3) × π × a × b × c, where a, b, and c are the three semi-principal axes.
How to find the volume of a Ellipsoid?
- 1Identify semi-principal axes a, b, and c (half of full axes lengths).
- 2Multiply a × b × c.
- 3Multiply by (4/3)π.
Example: Calculate the Volume of a Ellipsoid
Example 1: Find ellipsoid volume
Problem: An ellipsoid has semi-axes a = 3 cm, b = 4 cm, c = 5 cm.
Solution Steps:
- V = (4/3) × π × 3 × 4 × 5
- V = (4/3) × π × 60 = 80π ≈ 251.33 cm³
Final Volume:251.33 cm³
Frequently Asked Questions (FAQ)
Q: How is an ellipsoid related to a sphere?
A sphere is a special ellipsoid where all three semi-axes are equal (a = b = c = r).