Checked example
Worked calculation
Result: With r = 3 cm and h = 10 cm, the cylinder is 90π ≈ 282.743 cm³ and the cone is 30π ≈ 94.248 cm³.
01 • Guide
Same dimensions, fixed ratio
The one-third factor is independent of radius and height as long as both shapes share them. Changing either dimension scales both volumes together, so their 3:1 ratio stays constant.
Keep the full precision of intermediate values and round only the final display. This avoids compounding error when a derived radius or converted unit is used in another step.
02 • Guide
A geometric interpretation
Three congruent cone volumes can be rearranged conceptually to fill the matching cylinder. Integration reaches the same result by adding circular slices whose radii grow linearly from the cone tip.
The calculator validates physical limits before displaying a result. Blank or impossible inputs never produce a stale value, NaN or Infinity.
03 • Guide
Comparison graph
The result graph keeps height fixed and varies radius. Both curves grow with r², while the cone curve remains exactly one third as high at every point.
Interpretation
How to use the result responsibly
The answer models an ideal geometric cylinder. Manufacturing tolerances, wall thickness, rounded ends, deformation, tank tilt and measurement uncertainty can all shift a real value. Use inside dimensions for capacity and outside dimensions for occupied space. For safety, compliance, dosing, structural or purchasing decisions, compare the estimate with drawings, calibration data or a qualified professional.
Dimensional checks help catch mistakes: a volume result must carry cubic units, an area result square units and a derived radius or height linear units. If changing one unit alters the represented physical size, a conversion step was missed.