Problem 72 - Introductory Algebra for College Students

Question

Describe how volume is measured. Explain why linear or square units cannot be used.

Step-by-Step Solution

Answer

Volume is measured in cubic units because it accounts for the three dimensions - length, width, and height - that constitute the total space an object occupies. Linear (one dimensional) and area (two dimensional) measurements are not enough for this because they leave out one or two dimensions, respectively.

Step 1: Understanding Units Measurement

Volume is measured in cubic units. Cubic units constitute length, width, and height. Each of these dimensions is a linear measure, meaning it involves only one dimension. When considering two dimensions, we are looking at area measurements (square units) - length times width. However, to measure the amount of space an object occupies, we need to consider three dimensions - length, width, and height. Hence, cubic units are used.

Step 2: Why not Linear Units?

Linear units, such as meters and feet, measure the length of a line segment in one dimension only. So, they cannot account for the total space an object occupies, which involves three dimensions.

Step 3: Why not Area Units?

Area (square units), measures in two dimensions - length and width. It tells us about the size of the surface of the object. In the context of volume, an object's surface area does not provide enough information. We need not just the surface, but the space an object occupies in three dimensions. Here, area units leave out the dimension of height/depth, hence they cannot be used to measure volume.