Hemisphere Volume Examples: Solid Bowls vs Hollow Shells

Worked problems illustrating the difference between fluid capacity in a bowl and the volume of ceramic material in its walls.

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📅 Updated: October 13, 2026

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Solid vs Hollow Hemisphere Calculations

When calculating hemispheres, you must clarify whether you are finding:

Interior Capacity: The volume of liquid or air the hollow hemisphere holds.
Shell Volume: The volume of material (glass, metal, stone) used to manufacture the container.

A mixing bowl has an inner diameter of 20 cm (inner radius r = 10 cm). What is its maximum liquid capacity in liters?

V = (2/3) × π × 10³ = (2000 × 3.14159) / 3 ≈ 2,094.4 cm³

Since 1,000 cm³ = 1 Liter, capacity = 2.09 Liters.

Sphere Volume Formula

V = (4/3) × π × r³

Where V = Volume • r = Radius • π ≈ 3.14159265

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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