Count independent measurements
A box with volume 24 m³ could be 2 × 3 × 4 m, 1 × 3 × 8 m or many other shapes. Volume alone is insufficient. With length 2 m and width 3 m, however, height is 24 ÷ (2 × 3) = 4 m. Select “A missing dimension” and the named height-from-volume method. The main answer is Height in meters; the known volume remains an audit quantity, not a substitute for the answer you requested.
The missing height is a direction, not the known volume
The H ? arrow is the unknown perpendicular edge. L and W remain known edges. Known V is the whole solid’s volume, so it is not drawn as a length arrow.
| Step | Quantity or equation | Worked value |
|---|---|---|
| Known volume | V | 24 m³ |
| Known base edges | L = 2 m; W = 3 m | Base area LW = 6 m² |
| Requested height | H = V/(LW) | 24 m³ / 6 m² = 4 m |
| Forward check | L × W × H | 2 × 3 × 4 = 24 m³ |
| Insufficient information | V alone | Does not determine all three edges; do not guess missing dimensions |
Read diagram directions and numbered surface cues
- L: Length. Front horizontal edge; one of three perpendicular directions.
- W: Width. Receding base edge perpendicular to length and height.
- H: Height. Vertical edge perpendicular to both base edges.
- V: Known volume. Known volume of the entire declared solid; cubic units, not an edge.
- 1 ✓ Included: Side faces (four).
- 2 ✓ Included: Top face.
- 3 ✓ Included: Bottom face.
Solid outlines are schematic. Arrow endpoints identify the measurement; letters map to the table. ✓ included; × excluded; ? undetermined. Hidden edges use dashes.
Match the given surface definition
A cube with closed total surface 96 cm² has six equal square faces. Each face is 16 cm², giving edge 4 cm and volume 64 cm³. An open-top box or a curved cylinder surface is a different known quantity. Surface-based inverse methods in this calculator explicitly require their named closed total surface. Their forward check must agree with the supplied quantity. A contradictory or insufficient set of measurements produces an explanation rather than a guessed dimension.
Keep a geometric domain
A right cone with radius 3 cm and face slant 5 cm has perpendicular height √(25−9) = 4 cm. The slant must exceed the radius for a positive cone height. For a capsule, subtracting the two hemispheres’ sphere volume can give a zero straight section, which is explicitly a sphere boundary. Other unsupported zero or negative lengths are rejected. A square-pyramid slant is a face altitude and assumes a centered apex; a lateral edge is not interchangeable with it.
Check and carry the answer
After solving a supported missing dimension, the calculator recomputes the forward volume or closed surface. The primary output uses the actual dimension label and length or area unit, while the original volume and formulas remain below it. Check both the declared model and the named givens before copying the result. An inverse does not establish that a real container is safe, that an object fits a shipment or that a material order is appropriate. Those decisions need information outside this ideal geometric model.