Volume formulas for common solids
Volume is the three-dimensional space inside a solid, measured in cubic units. The standard formulas are:
box: V = length × width × height
cylinder: V = π × radius² × height
sphere: V = 4⁄3 × π × radius³
cone: V = 1⁄3 × π × radius² × height
pyramid: V = 1⁄3 × base area × height
Worked example
Volume of a cylinder, radius 3, height 10:
Square the radius: 3² = 9.
Multiply by π and height: π × 9 × 10 ≈ 282.74 cubic units.
Units and capacity
Keep every dimension in the same unit; the answer is in that unit cubed. To convert cubic units to liquid capacity: 1 cubic foot ≈ 7.48 US gallons, and 1 litre = 1,000 cubic centimetres.
Tip: a cone or pyramid is exactly one-third the volume of the cylinder or prism that boxes it in — a handy sanity check.