SOL014 · 3D solids & mensuration · Classes 11–12 + B.Tech
Ellipsoid
An ellipsoid is a stretched sphere with three semi-axes a, b, c. When a = b = c it is a sphere.
4/3 πabcEllipsoid
📐 Formula
V = 4/3 π a b c; x²/a² + y²/b² + z²/c² = 1
✏️ Worked example
a = 3, b = 2, c = 1.5: V = 4/3 × π × 9 ≈ 37.70.
🌍 Where it is used
Eggs, rugby balls, the shape of the Earth (slightly flattened).
❓ Quick check
Volume of an ellipsoid with a = b = c = 2?
🏋️ Practice
Easya = 1, b = 2, c = 3. Volume?
Answer: 8π ≈ 25.13
MediumIs a sphere an ellipsoid?
Answer: Yes, with a = b = c
ChallengeIs the Earth an exact sphere?
Answer: No: slightly flattened at the poles