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Chapter 2: Problem 83

When is it correct to use \(\mathrm{cm}^{3}\) instead of \(\mathrm{mL}\) ? Explain.

Short Answer

Expert verified
It is appropriate to use cubic centimeters (\(\mathrm{cm}^3\)) instead of milliliters (\(\mathrm{mL}\)) when working with solid objects or in scientific and technical situations where the dimensions are given in centimeters or meters. Examples include calculating the volume of a box or determining the volume of a cylinder. Since 1 \(\mathrm{cm}^3\) is equal to 1 \(\mathrm{mL}\), milliliters are preferred when measuring liquid volumes in everyday contexts such as cooking, laboratory measurements, and medicine dosages.

Step by step solution

01

Understand the units

First, let's understand the units: - A cubic centimeter (\(\mathrm{cm}^{3}\)) is a unit of volume derived from the metric system, where 1 \(\mathrm{cm}^{3}\) is equal to the volume of a cube with each side measuring 1 centimeter. - A milliliter (\(\mathrm{mL}\)) is also a unit of volume and is commonly used in measuring liquid volumes. It is part of the International System of Units and is derived from the base unit liter (\(\mathrm{L}\)). One milliliter is equal to one-thousandth of a liter or 0.001 liters.
02

Relationship between cm鲁 and mL

Now that we understand what each unit represents, let's look at their relationship. It turns out that the volume of 1 \(\mathrm{cm}^{3}\) is exactly equal to the volume of 1 \(\mathrm{mL}\). So, we can write this relationship as: 1 \(\mathrm{cm}^{3}\) = 1 \(\mathrm{mL}\)
03

Appropriate use of cm鲁

Cubic centimeters (\(\mathrm{cm}^{3}\)) are primarily used in scientific and technical contexts, such as calculating volumes of solids, measuring engine displacement, and other instances where an object's dimensions are given in centimeters or meters. Examples: - Calculating the volume of a box with dimensions 10cm x 8cm x 5cm - Determining the volume of a cylinder with radius 3cm and height 12cm
04

Appropriate use of mL

Milliliters (\(\mathrm{mL}\)) are commonly used in everyday situations to measure the volume of liquids, including in cooking, laboratory measurements, and medicine dosages. Examples: - Measuring 200 \(\mathrm{mL}\) of water to add to a recipe - Pipetting 10 \(\mathrm{mL}\) of a chemical solution in a lab experiment - Administering a 5 \(\mathrm{mL}\) dose of cough syrup
05

When to use cm鲁 instead of mL

Given their equivalence and the contexts in which they are typically used, it is appropriate to use cubic centimeters (\(\mathrm{cm}^{3}\)) instead of milliliters (\(\mathrm{mL}\)) when working with solid objects or in scientific and technical situations where the dimensions are given in centimeters or meters. In other situations that involve the measurement of liquids in everyday contexts, milliliters would be the preferred unit of measurement.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cubic Centimeters
Cubic centimeters (cm^3 or cc) are a common unit of volume that you will encounter in scientific and technical fields. As each side of this cube measures one centimeter, imagine a tiny cube that could fit on the tip of your finger; that's the physical representation of a cubic centimeter.

In practice, cubic centimeters are most often used when describing the volume of solid objects. For instance, if you're measuring the size of a small box or the displacement of a car's engine, cubic centimeters can offer a precise volume measurement. This unit is also handy when dealing with 3D shapes that have their dimensions provided in centimeters, facilitating direct computation without conversions.
Milliliters
Milliliters (mL) are equally significant in volume measurement, particularly when it comes to liquids. As part of the International System of Units (SI), milliliters provide a connection to the base unit of liter, which is more broadly applied for liquid volumes.

The milliliter is useful and prevalent in our daily lives鈥攚hether it's for cooking, where we measure ingredients, or in the medical field, where precise dosages of medication are crucial. A milliliter represents a volume equal to the space inside a cube that measures 1 centimeter on each side, which is fascinatingly the same physical space as a cubic centimeter. This dual representation emphasizes the versatility of volume measurement in different contexts.
Scientific Measurement
Scientific measurement is a cornerstone of experimentation and innovation, requiring accuracy, precision, and a standard system understood across the globe. It involves the systematic and repeatable quantification of properties and phenomena using defined units of measurement.

The adherence to such standards enables scientists and engineers to communicate findings without ambiguity. Volume measurement is just one aspect of this meticulous process, where units like cubic centimeters and milliliters are applied according to the nature of the substance (solid or liquid) and the context (technical or everyday use).
Metric System
The metric system, a global standard for measurement, defines units like cubic centimeters and milliliters, facilitating uniformity and ease of understanding. Developed during the French Revolution, this system is based on multiples of 10, making calculations more straightforward than those required by the Imperial or US customary systems.

Cubic centimeters and milliliters are integral parts of this system, representing volume for solids and liquids respectively. The metric system is built on base units such as meters for length, kilograms for mass, and seconds for time, with all other units being multiples or fractions of these. Understanding the metric system is essential for engaging with the disciplines of science and engineering, which are rich with measurements and calculations.

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Most popular questions from this chapter

To the correct number of significant figures, what is the product of each mathematical operation? Use scientific notation when necessary. (No units shown means a number is exact.) (a) \(2.30 \mathrm{~cm} \times 2\) (b) \(2 \mathrm{~m} \times 2.000 \mathrm{~m}\) (c) \(1001 \mathrm{~J} \times 10\) (d) \(124 \mathrm{~mm} \div 0.1 \mathrm{~mm}\)

Gold has a density of \(19.3 \mathrm{~g} / \mathrm{mL}\). Suppose you have \(100.0\) glonkins of gold. What volume in liters will the gold occupy? Here are some conversion factors to help you: \(0.911\) ounce per glonkin and \(28.35 \mathrm{~g}\) per ounce. Use unit analysis to calculate your answer, and show your work. Treat both conversion factors as exact.

A student uses a digital balance to determine the mass of an object. Its digital display reads \(2.635 \mathrm{~g}\). He keeps looking at the balance and it stays fixed at \(2.635 \mathrm{~g}\) for half an hour. He then states, "The mass of the object is \(2.635 \mathrm{~g}\) exactly. There is no uncertainty in this measurement because the last digit '5' stayed constant and did not change over time." Is he right? Is the mass of the object exactly known with no uncertainty? Explain.

Indicate the correct number of significant figures for each answer, given that all values are measurements: (a) \(\left(6.350 \times 10^{-8}\right) \times(0.0080)\) (b) \(\left(5.30 \times 10^{2}\right)+\left(22.1 \times 10^{2}\right)\) (c) \(\left(5.830 \times 10^{2}\right)+\left(22.100 \times 10^{2}\right)\) (d) \(\frac{100.0 \times 0.1500}{58.443}\) (e) \(\frac{100.0 \times 0.15}{58.4}\)

The density of gold is \(19.3 \mathrm{~g} / \mathrm{mL}\), that of lead is \(11.4 \mathrm{~g} / \mathrm{mL}\), that of iron \(7.8 \mathrm{~g} / \mathrm{mL}\), and that of aluminum \(2.7 \mathrm{~g} / \mathrm{mL}\). A student is given separate samples of three substances \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), along with a graduated cylinder containing \(50.0 \mathrm{~mL}\) of water. Each sample has a mass of \(200.0 \mathrm{~g}\), and the student finds that the volumes of the samples are A, \(25.64 \mathrm{~mL} ; \mathrm{B}, 10.36 \mathrm{~mL} ;\) and \(\mathrm{C}, 17.54 \mathrm{~mL}\). What is the identity of each substance?
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