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Calculate the volume of common 3D shapes: cube, rectangular box, cylinder, sphere, cone, square pyramid, and triangular prism.
Volume Formulas:
Cube: V = a³
Box: V = l × w × h
Cylinder: V = π × r² × h
Sphere: V = (4/3) × π × r³
Cone: V = (1/3) × π × r² × h
Square Pyramid: V = (1/3) × a² × h
Triangular Prism: V = (1/2) × b × ht × l
Volume measures the amount of three-dimensional space an object occupies. It is expressed in cubic units (cm³, m³, in³, ft³, etc.).
Multiply the area of the circular base by the height: V = π × r² × h, where r is the radius and h is the height. For example, a cylinder with radius 5 and height 10 has volume ≈ 785.4 cubic units.
Both use V = (1/3) × base area × height. For a cone, the base area is π × r². For a square pyramid, the base area is a² (side squared). The factor of 1/3 appears in both because the volume is one-third of the enclosing prism/cylinder.
Use V = (4/3) × π × r³ where r is the radius. For a sphere with radius 5: V = (4/3) × π × 125 ≈ 523.6 cubic units.
The calculator uses whatever units you enter. If you enter dimensions in centimeters, the result is in cubic centimeters. There is no unit conversion — be consistent with your units across all inputs.