zztool Sphere Volume Formula
A sphere is a 3D geometric shape where all points on the surface are equidistant from the center. The volume formula is V = (4/3)πr³, where r is the radius. The surface area formula is A = 4πr². If diameter d is known, then r = d/2.
Formulas
Volume FormulaV = (4/3)πr³ = (π/6)d³
Surface Area FormulaA = 4πr² = πd²
Radius & Diameterd = 2r, r = d/2
Examples
Radius r = 5
V = (4/3)π×5³ ≈ 523.6
A = 4π×5² ≈ 314.16
Diameter d = 10
V = (π/6)×10³ ≈ 523.6
A = π×10² ≈ 314.16
Tips
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FAQ
How is the sphere volume formula derived?
The sphere volume formula can be derived using calculus by integrating circular cross-sections along the height, resulting in V = (4/3)πr³.
What is the relationship between radius and diameter?
Diameter is twice the radius (d = 2r). Radius is the distance from center to surface, diameter is the longest line through the center.
How to calculate hemisphere volume?
Hemisphere volume is half of a full sphere: V = (2/3)πr³.
How to calculate sphere surface area?
Sphere surface area formula is A = 4πr², which equals the area of 4 great circles.
Last Updated: 2026-06-04✓ Expert Verified
Great for 3D calculations!
Calculates volume and surface area.
Very helpful for math.