Question

a. List two SI-derived units for volume. b. List two non-SI units for volume, and explain how they relate to the cubic centimeter.

Short answer

Two SI-derived units for volume are cubic meters \((m^3)\) and liters \((L)\). Two non-SI units for volume include the cubic inch (≈16.387 cm³) and the gallon (≈3785 cm³).

Step-by-step solution

Identify SI-derived Units for Volume

SI-derived units are units that are derived from the seven base units of the International System of Units. For volume, one commonly used SI-derived unit is the cubic meter \((m^3)\). Another SI-derived unit for volume is the liter \((L)\), which is equal to a cubic decimeter \((dm^3)\).

Identify Non-SI Units for Volume

Non-SI units are units that are not officially part of the International System of Units but are frequently used in practice. One non-SI unit for volume is the cubic inch. Another common non-SI unit for volume is the gallon.

Explain the Relationship to the Cubic Centimeter

A cubic centimeter \((cm^3)\) is a unit of volume that is equivalent to \((10^{-6} m^3)\). One cubic inch is equal to approximately 16.387 cubic centimeters. Similarly, one gallon is equal to approximately 3,785 cubic centimeters.

Key concepts

SI-derived units

SI-derived units are units that are derived from the seven base units of the International System of Units (SI). These derived units are formed by combining base units according to the rules of algebra. For volume, one of the most common SI-derived units is the cubic meter \(m^3\). This unit is derived from the meter, the base unit of length in the SI system. Another significant SI-derived volume unit is the liter \(L\), which is defined as a cubic decimeter \(dm^3\). Thus, one liter is equal to 0.001 cubic meters \(1 L = 10^{-3} m^3\).
These units are important because they provide a standardized way to measure volume, making it easier to compare different quantities and perform calculations in science and engineering.

Non-SI units

Non-SI units are units of measurement that are not part of the official International System of Units (SI). Despite not being standardized within the SI framework, they are still commonly used in everyday life and certain industries. Two prevalent non-SI units for volume are the cubic inch and the gallon.
The cubic inch is a unit commonly used in the United States, especially in measuring the volume of engine cylinders. It represents the volume of a cube with each side measuring one inch.
The gallon is another non-SI unit mostly used in the United States for liquid volumes like gasoline and milk. One gallon is substantially larger than a cubic inch and equals approximately 231 cubic inches or 3.785 liters. These units provide a practical means for volume measurement in specific contexts, even though they do not belong to the SI system.

Volume measurement

Volume measurement refers to the process of quantifying the three-dimensional space occupied by a substance. It is crucial in various fields such as chemistry, physics, engineering, and everyday tasks like cooking and filling up a gas tank.
There are different units of volume in use, categorized as SI-derived and non-SI units. SI-derived units like cubic meters \(m^3\) and liters \(L\) enable scientists and engineers to perform calculations and communicate results unambiguously. Meanwhile, non-SI units like cubic inches and gallons are often more familiar to the general public and are used in specific regions or industries.
Understanding volume measurement involves knowing how to convert between these units, ensuring accuracy and consistency whether working in scientific research or day-to-day activities.

Cubic centimeter

A cubic centimeter \(cm^3\) is a unit of volume in the metric system, and it represents the volume of a cube with each side measuring one centimeter. One cubic centimeter is equivalent to \(10^{-6} m^3\).
This unit is particularly useful in medicine, chemistry, and automotive industries, as it provides a convenient way to express small volumes. For instance, engine sizes are often measured in cubic centimeters (cc) in the automotive industry.
When converting non-SI units to cubic centimeters, it's essential to know the specific conversion factors. For example, one cubic inch is approximately equal to 16.387 cubic centimeters. Similarly, one gallon is approximately 3,785 cubic centimeters. These conversions help bridge the gap between different measurement systems and ensure precision in volume-related calculations.