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Chapter 1: Problem 69

Change \(1 \mathrm{~m}^{3}\) to \(\mathrm{L}\).

Short Answer

Expert verified
1 cubic meter equals 1000 liters.

Step by step solution

01

Understanding Cubic Meters

A cubic meter, denoted as \(1 \mathrm{~m}^3\), is a unit of volume in the metric system. It represents the volume of a cube with sides of length 1 meter.
02

Conversion Factor

We need to know the conversion factor between cubic meters and liters. By definition, \(1 \mathrm{~m}^3\) is equivalent to \(1000\) liters.
03

Applying the Conversion

Using the conversion factor, we multiply the volume in cubic meters by \(1000\) to convert it to liters. Therefore, \(1 \mathrm{~m}^3 \times 1000 = 1000 \text{ liters}\).

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Key Concepts

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

Cubic Meter
The cubic meter, symbolized as \(1 \mathrm{~m}^3\), is a standard unit of volume in the metric system that is used worldwide. This unit of measurement helps quantify the space occupied by an object, which is a cornerstone concept in studies involving density and capacity. Imagine a cube with all sides measuring 1 meter in length. This cube represents exactly one cubic meter.
  • The cubic meter is often used in measuring spaces like rooms in a building or the capacity of containers.
  • This unit helps keep calculations simple and related directly to physical dimensions.
It is essential to understand that a cubic meter covers not just the surfaces of the cube but the entire volume inside.
Liter
A liter, abbreviated as \(\mathrm{L}\), is another important unit of volume in the metric system. It is widely used for measuring liquids or other non-solid substances. When you pour a liter of water into a container, you are filling the container up to absolute capacity, assuming it holds exactly one liter.
  • 1 liter is equivalent to 1 cubic decimeter (\(1 \mathrm{~dm}^3\)).
  • This relation allows us to easily switch between using liters and cubic measurements when converting liquid volumes.
Knowing how many liters a container can hold is crucial in contexts like cooking, scientific experiments, or even when fueling vehicles.
Metric System
The metric system is an internationally recognized system for measuring and converting various physical quantities. It is based on units of ten, which simplifies calculations and conversions, making it especially valuable in scientific research, industry, and everyday life.
  • Standard units in the metric system include meters for length, kilograms for mass, and liters for volume.
  • The system's universality makes it easier for people across different regions and disciplines to communicate measurements without confusion.
The metric system's logical structure and ease of use have led to its adoption all over the world, particularly for scientific and technical fields, ensuring consistency in units and conversions, such as between cubic meters and liters.

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Most popular questions from this chapter

Determine the accuracy (the number of significant digits) of each measurement. \(1.20 \times 10^{-5} \mathrm{~ms}\)

Use the rules for division of measurements to divide. $$ \frac{347 \mathrm{~km}}{4.6 \mathrm{~h}} $$

Use the rules for addition of measurements to add each set of measurements. $$ \begin{array}{r} 8,560 \mathrm{~m} \\ 84,000 \mathrm{~m} \\ 18,476 \mathrm{~m} \\ 12,500 \mathrm{~m} \\ \hline \end{array} $$

Change 4 h 25 min 15 s to s.

Use the rules for addition of measurements to add each set of measurements. $$ 6800 \mathrm{ft} ; 2760 \mathrm{ft} ; 4 \overline{0} 00 \mathrm{ft} ; 20 \overline{0} 0 \mathrm{ft} $$
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