Sphere Volume

Sphere vs Hemisphere: Formulas, Volumes & Differences

Comprehensive side-by-side comparison of full spheres and hemispheres, including solid vs hollow surface area considerations.
👤 By Administrator
📅 Updated: October 13, 2026
⏱ 2 min read
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Comparing Spheres and Hemispheres

A hemisphere is created by bisecting a sphere along any plane that passes through its geometric center. While calculating volume is straightforward (exactly half), calculating surface area requires careful attention to whether the hemisphere is hollow or solid.

Mathematical Formula Comparison

PropertyFull SphereSolid HemisphereHollow Hemisphere
Volume (V)4/3 π r³2/3 π r³2/3 π (r_outer³ - r_inner³)
Curved Area4 π r²2 π r²2 π r²
Base Disc AreaNone (0)π r²None (open)
Total Area4 π r²3 π r²2 π r²
Sphere Volume Formula

Sphere Volume Formula

V = (4/3) × π × r³
Where V = Volume • r = Radius • π ≈ 3.14159265

Essential Mathematical Notation

  • V Volume of the sphere — The three-dimensional space enclosed within the spherical surface, measured in cubic units (e.g., cm³, m³, in³, ft³).
  • r Radius of the sphere — The straight-line distance from the exact center to any point on the outer surface (r = d / 2).
  • π Pi (π) — The mathematical circle constant, approximately 3.14159265 (or 22/7).
  • 4/3 Geometric Constant (4/3) — The rational coefficient derived from spherical calculus integration.
  • r³ Radius Cubed (r³) — The radius multiplied by itself three times (r × r × r), measuring 3D volume.
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