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Calculate the volume of rectangular prisms

Volume measures the three-dimensional space occupied by a rectangular prism and is calculated by multiplying its length, width, and height, V=lwhV = lwh, using consistent units and reporting the result in cubic units. Layers or arrays of unit cubes explain why the three dimensions are multiplied, including when measurements are whole numbers, decimals, or simple fractions; the scope excludes composite solids, nonrectangular solids, and more generalized algebraic treatments.

Detailed Explanation: Calculate the volume of rectangular prisms

A rectangular prism is a box-shaped solid. Its volume is the amount of space inside it.

Use the formula:

V=lwhV=lwh

where:

  • ll is the length,
  • ww is the width,
  • hh is the height.

Multiplying the three dimensions works because the prism can be filled with layers of unit cubes. Each layer has l×wl \times w cubes, and there are hh layers.

Example: A rectangular prism has a length of 88 cm, a width of 33 cm, and a height of 55 cm. Find its volume.

  1. Write the formula:

V=lwhV=lwh

  1. Substitute the measurements:

V=(8)(3)(5)V=(8)(3)(5)

  1. Multiply:

8×3=248 \times 3=24 24×5=12024 \times 5=120

  1. Include cubic units because volume measures three-dimensional space:

120 cm3\boxed{120\text{ cm}^3}

The volume of the rectangular prism is 120120 cubic centimeters.

Learn by doing: Calculate the volume of rectangular prisms

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    Volume of a Rectangular Prism - Calculate

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