The Volume of Solids Using Algebra

The volume of a solid can be expressed using algebraic expressions. In this case, the measurements necessary for the calculations are expressed by monomials or polynomials. To solve this type of problem, a maximum of two variables are used to define the different measurements.

The volume of a solid relates to the space it occupies. It is possible to express the volume as an algebraic expression if the solid’s measurements are defined by variables or algebraic expressions. Thus, it is important to refer to the different formulas for calculating the volume of solids.

Sometimes a solid has missing measurements, in which case they are represented using variables or algebraic expressions. These algebraic expressions may be provided or it may be necessary to find them by mathematically translating the statement. A simplified algebraic expression can be obtained by applying the formulas for calculating volume.

The following example illustrates a problem where the algebraic expressions are given.

The following example presents a problem where it is necessary to determine the algebraic expressions by mathematically translating the statement.

​​​By associating algebraic expressions and variables with different measurements, it is possible to obtain the dimensions of all the solids that respect the constraints stated in the problem.

With a little more information, the numerical value associated with the variable used can be found.

Sometimes, none of the measurements are known, in which case algebraic expressions can be used to define the missing measurements. The advantage of using algebra is that it provides several possible answers.