/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 How many cubic millimeters \(\le... [FREE SOLUTION] | 91Ó°ÊÓ

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How many cubic millimeters \(\left(\mathrm{mm}^{3}\right)\) are in \(1 \mathrm{L} ?\)

Short Answer

Expert verified
1 liter equals 1,000,000 cubic millimeters

Step by step solution

01

Understand the relationship between liters and cubic millimeters

1 litre is defined as the volume of a cube that measures 10 cm on each side which is equal to 1,000 cubic centimeters. And since 1 cubic centimeter is equal to 1,000 cubic millimeters, then 1 litre equals 1,000,000 cubic millimeters.
02

Execute the conversion

So in this case, since the given volume is 1 litre, it can be directly converted to cubic millimeters using the conversion factor. Thus, 1 liter equals 1,000,000 cubic millimeters.

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Key Concepts

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

Volume Measurement
Volume measurement is the process of determining how much three-dimensional space an object or substance occupies. It involves using specific units to quantify the space within an enclosure, like a container or a geometric shape.
When talking about volume, it's crucial to understand the connection between volume and dimensions. For example, if you have a box, you'll measure its length, width, and height. The product of these three values gives you the volume of the box.
Different units are used to measure volume, depending on the context or system being used. It's often expressed in units such as liters, cubic centimeters, or gallons. Each of these units has a specific application based on the object's size and the conventional measurement system of a given area or field.
It's also fascinating to know that volume can be measured for solids, liquids, and gases. Each has its approach, yet the central concept remains the same: identifying and understanding the space they fill. Understanding volume is essential for various practical applications, from determining how much liquid a bottle can hold to calculating space inside a room.
Metric System
The metric system is a decimal-based system for measuring length, mass, and volume. It's widely used around the world and known for its simplicity, as each unit is based on powers of ten.
For measuring volume, the metric system uses liters primarily, along with milliliters and cubic meters. The straightforward nature of the metric system makes it easy to convert between different units. For instance, 1 liter equals 1,000 milliliters or 1,000,000 cubic millimeters.
  • Length is measured in meters or centimeters.
  • Mass is measured in grams or kilograms.
  • Volume is measured in liters or cubic meters.
This consistency allows for easy calculations, understanding, and teaching, making it both a favorite and practical choice in education, science, and engineering.
The metric system's configuration provides clarity and uniformity in measurements. This helps avoid confusion and errors common in systems that don't use a standardized conversion method like the metric system.
Cubic Millimeters
Cubic millimeters are a unit of volume that belongs to the metric system. They are especially useful when dealing with very small volumes.
A cubic millimeter \((mm^3)\) signifies the volume of a cube with each side measuring precisely 1 millimeter. They provide a fine granulated measurement scale useful in detailed scientific calculations, engineering projects, and medical applications.
To visualize, imagine a small cube the size of a sugar crystal, that is roughly in the order of cubic millimeters. In everyday contexts, cubic millimeters are used less frequently compared to larger units like liters or milliliters, but they play a vital role in precise measurements. For instance, they may be used in contexts such as manufacturing mechanical parts to tight specifications or calculating the dosage of a medication.
Understanding cubic millimeters' relationship with other metric units is vital. Knowing that 1 cubic centimeter equals 1,000 cubic millimeters can greatly assist in converting measurements for various applications.

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Most popular questions from this chapter

\(\mathrm{A} 1.0 \mathrm{cm}^{3}\) air bubble is released from the sandy bottom of a warm, shallow sea, where the gauge pressure is 1.5 atm. The bubble rises slowly enough that the air inside remains at the same constant temperature as the water. a. What is the volume of the bubble as it reaches the surface? b. As the bubble rises, is heat energy transferred from the water to the bubble or from the bubble to the water? Explain.

When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist upper airways. When a person breathes dry air, about 25 mg of water are exhaled with each breath. At 12 breaths/min, what is the rate of energy loss due to evaporation? Express your answer in both watts and Calories per day. At body temperature, the heat of vaporization of water is \(L_{\mathrm{v}}=24 \times 10^{5} \mathrm{J} / \mathrm{kg}\).

How much energy must be removed from a 200 g block of ice to cool it from \(0^{\circ} \mathrm{C}\) to \(-30^{\circ} \mathrm{C} ?\)

The ocean is mostly heated from the top, by light from the sun. The warmer surface water doesn't mix much with the colder deep ocean water. This lack of mixing can be ascribed to a lack of A. Conduction. B. Convection. C. Radiation. D. Evaporation.

Some jellyfish can eject stingers with remarkable force and speed. One species does this by building up a 15 MPa gauge pressure that pushes against the base of a \(2.0-\mu \mathrm{m}\) -diameter stylet, forcing it outward. a. What force does the excess pressure exert on the stylet? b. The mass set into motion is a tiny \(1.0 \times 10^{-12} \mathrm{kg} .\) What is the resulting acceleration?

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