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Find a missing dimension from volume

Volume measures the space occupied by a rectangular prism and can be represented as the product of its length, width, and height. Given the volume and two dimensions, the missing dimension is found by dividing the volume by the product of the known dimensions, while maintaining consistent cubic and linear units; this distinguishes volume from surface area and supports reasoning about inverse relationships in measurement.

Detailed Explanation: Find a missing dimension from volume

The volume of a rectangular prism is found by multiplying its three dimensions:

V=l×w×hV = l \times w \times h

To find a missing dimension:

  1. Multiply the two known dimensions.
  2. Divide the volume by that product.
  3. Label the answer with linear units, such as centimeters or meters.

Example: A rectangular prism has a volume of 120 cm3120\text{ cm}^3, a length of 6 cm6\text{ cm}, and a width of 4 cm4\text{ cm}. What is its height?

Start with the volume formula:

V=l×w×hV = l \times w \times h

Substitute the known values:

120=6×4×h120 = 6 \times 4 \times h

Multiply the known dimensions:

6×4=246 \times 4 = 24

Now divide the volume by 2424:

h=12024=5h = \frac{120}{24} = 5

The missing height is:

5 cm\boxed{5\text{ cm}}

Check: 6 cm×4 cm×5 cm=120 cm36\text{ cm} \times 4\text{ cm} \times 5\text{ cm} = 120\text{ cm}^3, so the answer is correct. Notice that volume uses cubic units, while the missing dimension uses regular linear units.

Learn by doing: Find a missing dimension from volume

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    Volume of a Rectangular Prism - Calculate Side from Volume and Sides

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