Problem 72 - Introductory and Intermediate Algebra for College Students 4th

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's a three-dimensional measure. Linear units (1D) and square units (2D) cannot be used as they do not have the capacity to accurately measure three-dimensional space.

Step 1: Understanding Measurement Units

Volume is a measure of the amount of space an object or substance occupies. It is quantified numerically using the cubic units. A cubic unit of measurement in three dimensions is needed because we are dealing with three different directions: length, width, and height. Hence, the unit for measuring volume is cubic units, like cubic centimeters (cm³), cubic meters (m³), cubic inches (in³), etc.

Step 2: Understanding Linear and Square Units

Linear measurements are one-dimensional measurements. They only consider one line of direction (length, width or height) such as meters, centimeters, feet, etc. On the other hand, square units are used for measuring area, which is a two-dimensional measurement. This incorporates two directions (length and width). For instance, square meters (m²), square centimeters (cm²), etc.

Step 3: Why Linear or Square Units Cannot be Used for Measuring Volume

Linear measurements are confined to one dimension while square units apply to two dimensions. But volume, being a three-dimensional property, requires a three-dimensional unit for its measurement — which is the cubic unit. Therefore, it wouldn't make sense to use linear or square units to measure volume as they lack the necessary dimensional capacity.