Geometry
Recovering a missing dimension from the volume
Divide the known volume by the area of the known base. The same rearrangement finds length or width if either is the unknown instead.
The Formula
h = V / (l x w)
Divide the known volume by the area of the known base. The same rearrangement finds length or width if either is the unknown instead.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| V | Known volume | cubic units | Must be in cubic units matching those of the two known edges. |
| l x w | Area of the known base | square units | 1200 square centimetres when length is 40 and width is 30. |
| h | The unknown third dimension | length | 24000 divided by 1200 gives 20, recovering the original height exactly. |
What Each Symbol Means
Vcubic units
Known volume
Must be in cubic units matching those of the two known edges.
l x wsquare units
Area of the known base
1200 square centimetres when length is 40 and width is 30.
hlength
The unknown third dimension
24000 divided by 1200 gives 20, recovering the original height exactly.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the volume of a rectangular prism page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Volume Of A Rectangular Prism, filed under Math. Every number the guide produces comes from substituting into this one line.