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Find volume of rectangular prisms

Volume of a rectangular prism represents the three-dimensional space it occupies, measured in cubic units; arranging unit cubes in equal layers explains why V=l×w×hV = l \times w \times h, rather than adding the dimensions or using a square-unit measure. The learner finds volume and, when appropriate, a missing dimension for prisms with whole-number, decimal, or fractional edge lengths, using consistent units; general prisms and advanced algebraic volume formulas are outside this scope.

Detailed Explanation: Find volume of rectangular prisms

Volume measures the amount of three-dimensional space inside a rectangular prism. Imagine filling the prism with unit cubes. The cubes form equal layers, so:

V=l×w×hV=l\times w\times h

The answer is written in cubic units, such as cm3\text{cm}^3 or m3\text{m}^3.

Example: A rectangular prism is 4.5 cm4.5\text{ cm} long, 3 cm3\text{ cm} wide, and 2 cm2\text{ cm} high. Find its volume.

  1. Identify the three dimensions:

l=4.5 cm,w=3 cm,h=2 cm l=4.5\text{ cm},\qquad w=3\text{ cm},\qquad h=2\text{ cm}

  1. Substitute them into the formula:

V=4.5×3×2 V=4.5\times3\times2

  1. Multiply:

4.5×3=13.5 4.5\times3=13.5 13.5×2=27 13.5\times2=27

  1. Include cubic units:

V=27 cm3 \boxed{V=27\text{ cm}^3}

The volume is 27 cm327\text{ cm}^3. This means the prism could hold 2727 unit cubes that each measure 1 cm1\text{ cm} on every side. Notice that volume uses all three dimensions and has cubic units, not square units.

Learn by doing: Find volume of rectangular prisms

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    Volume of a Rectangular Prism - Calculate

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