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Linear to Cubic Conversion

Converting linear measurements into cubic ones is a fairly simple procedure that has been around for thousands of years. Officials in ancient Babylon and Egypt had to determine how much grain might fit in a storage pit of certain dimensions, just as a homeowner in the 21st century might have to decide how much heating oil can go in a storage tank or how much water is needed to fill a swimming pool. In all these cases, the solution is arrived at by simply multiplying the dimensions.
  1. Dimensions

    • Linear measurements only have one dimension, while cubic measurements are of three-dimensional units. To make a meaningful conversion, you must have three linear measurements, such as length, width and height, or a combination of linear and area measurements if you know the length of one side and the area of a base. You cannot have a cubic measurement of a line or a flat surface because it only has one and two dimensions, respectively.

    Rectangular Shapes

    • The simplest type of conversion from linear to cubic measurements occurs when we determine the volume of a rectangular prism, which is a six-sided three-dimensional figure in which each side is a rectangle. Basically, a rectangular prism is a box, with a width, a length and a height. You find the cubic measurement of the shape by multiplying those three dimensions together. For instance, a rectangular prism that was 8 inches long, 6 inches wide and 4 inches high would have a volume of 192 cubic inches. Another way to look at it is to say that you are multiplying the height times the area of the base to get the volume. Using the same box, you could find the cubic measurement by multiplying the height (4 inches) by the area of the base (6 inches times 8 inches, or 48 square inches).

    Cylindrical Shapes

    • Not all three-dimensional objects have rectangular bases. A cylinder, for instance, has length, but the base is a circle. To find the cubic volume of a cylinder, you would multiply its length by the area of the base (πr²). A cylinder that is 8 meters long with a circular base that has a radius of 2 meters, would have a volume of 8·π·2² m³, or approximately 100.54 m³.

    Units of Measurement

    • An important consideration when converting linear measurements to cubic is the unit of measurement. An inch is a one-dimensional unit of length. A square inch (in²) is a two-dimensional measure of area. A cubic inch (in³) is a three-dimensional measure of volume. When the number of dimensions is changed, the unit of measure must change with it.

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