Geometry

Hemisphere Geometry: Volume & Surface Area Properties

A hemisphere is formed by cutting a sphere into two equal halves through its center plane.
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📅 Updated: October 13, 2026
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Understanding the Hemisphere

When a sphere is divided along its great circle equator, two congruent solid hemispheres are created. Hemispheres are foundational in architectural dome design, astronomy, and acoustic engineering.

Volume Formula

Because it is exactly half of a full sphere, its volume is calculated as:

V = 2/3 × π × r³

Curved vs Total Surface Area

A solid hemisphere possesses two distinct surfaces: the curved dome and the flat circular base.

  • Curved Surface Area: A_curved = 2πr²
  • Base Circular Area: A_base = πr²
  • Total Surface Area (Solid): A_total = 2πr² + πr² = 3πr²
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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