Units of Volume

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Units of Volume

In this text, we will focus on units of volume, a critical concept for understanding space and measurement. We will explore unit cubes and cubic units, and familiarize ourselves with different volume units such as cubic centimeters ($\text{cm}^3$), cubic inches ($\text{in}^3$), and cubic feet ($\text{ft}^3$).

Understanding Units of Volume

Volume measures how much space an object occupies. It relates to three-dimensional shapes, and is expressed in cubic units. It is important to remember that volume considers the height, length, and width of an object.

A cubic unit is how much space is inside a shape with each side the same length. It's like a box made out of blocks, where each block is the same size.

To measure volume, we use cubes because volume is about filling space in three dimensions: length, width, and height. A cube has all three (length x width x height), making it perfect for measuring volume. We write this as ³, which means cubed.

Before progressing, let’s check your understanding so far.

What kind of shapes is volume often used with?
What does a cubic unit represent?
Why do we measure volume in cubes?

Units of Volume – Types and Differences

When measuring volume, we often use different units depending on the size of the object. It is important to consider what unit of volume makes most sense when measuring objects. These units are all based on cubes of different sizes. Here's a look at the main types:

• Cubic Centimeter ($\text{cm}^3$): This unit is used for small objects. It's a cube where each side is 1 centimeter long. Imagine a tiny sugar cube, that's about a cubic centimeter.
• Cubic Inch ($\text{in}^3$): A bit larger, this is a cube with each side measuring 1 inch. It’s like a small toy block.
• Cubic Foot ($\text{ft}^3$): This is much bigger, used for large items or spaces. A cubic foot is a cube where each side is 1 foot long. Think of a storage container or box.
• Cubic Meters ($\text{m}^3$): This unit is used for larger items or spaces. A cubic meter is a cube where each side is 1 meter long. Think of a swimming pool for this size.

Units of Volume – Table

Below is a table of the different units of volume measurement and their common uses. It is important to remember that this is a partial list of measurements that can be used with volume.

Unit of Volume Size of Each Side of the Cube Common Use
Cubic Centimeter ($\text{cm}^3$) 1 cm Small objects like a dice
Cubic Inch ($\text{in}^3$) 1 in Medium objects like a toy block
Cubic Foot ($\text{ft}^3$) 1 ft Large spaces like a storage box
Cubic Meters ($\text{m}^3$) 1 m Larger spaces like a swimming pool

Relationship between Liters and Centimeters in Volume

A liter and a cubic centimeter ($\text{cm}^3$) measure volume, which is how much space something takes up. Think of a $\text{cm}^3$ as a tiny box. A liter is a much bigger box. To fill this big box with tiny boxes, you would need 1,000 of them. So, 1 liter is the same as 1,000 cubic centimeters. This helps us understand and compare the size of different things easily!

Units of Volume – Guided Practice

When working with units of volume, it is important to apply logical thinking and reasoning skills. The steps you can use to think this through are:

• Step 1: understand the size
• Step 2: Know the unit you will use
• Step 3: Apply the unit

Let’s have a go together by applying this logical thinking and reasoning to a swimming pool.

Why do we use cubic meters ($\text{m}^3$) to measure the volume of water in a swimming pool?

Units of Volume – Application

Consider various objects like a sugar cube, a shipping box, and a room. Think about which unit of volume would be most suitable for each and why.

Which unit of volume would you use for a sugar cube?
Which unit of volume would you use for a shipping box?
Which unit of volume would you use to measure a room?

Units of Volume – Summary

Key Points from this Text:

• Cubic units are fundamental in measuring volume.

• Common units include cubic centimeters, cubic inches, and cubic feet.

• Choosing the right unit depends on the size of the object or space.

Volume is an important concept, and your journey in understanding units of volume today is just the beginning! You may want to explore how to calculate the volume of rectangular prisms, spheres, cones or cylinders where you can begin applying your learning about units of volume!

Units of Volume – Frequently Asked Questions

What is a cubic meter?
Can volume be measured in liters?
Is a cubic yard a common unit of volume?
How do you visualize a cubic unit?
Why are different units of volume used?
Are cubic units used in everyday life?
Can cubic units be converted to other units?
What is the significance of the cubic centimeter in medicine?
How are cubic inches used in engineering?
What is an improvised unit of volume?

TranscriptUnits of Volume

You may not even realize it, but volume is all around us, shaping the very essence of our existence. But how do we measure this captivating concept? Let’s dive right in, and learn about units of volume. Volume is a measure of how much space an object takes up. It helps us understand how much of something can fit inside a particular object or container. Therefore, volume is an essential concept in our daily lives. Now, when it comes to measuring volume, we use different units for liquids and solids. Let's explore them further! When we talk about measuring the volume of liquids, we can use metric units like milliliters and liters. Milliliters are used for smaller amounts of liquid, like a small cup of juice. Liters are used for larger amounts of liquid, like a jug of water. In the US, we can also use customary units such as fluid ounces, quarts, and gallons. Fluid ounces and quarts can also be used for smaller volume measurements, like a cup of juice. Gallons can also be used to measure greater volumes of liquid, like a gallon of milk. Now let's take a look at volumes of solid objects. For measuring the volume of solid objects, we can use metric measurements such as cubic centimeters and cubic meters, and customary units such as cubic inches and cubic feet. Cubic is represented by this exponential three we see next to the measurements. The smaller units of measurement for both metric and customary can be used for smaller objects, such as a die, or a sugar cube. The larger units of measurement for both metric and customary can be used for larger objects, such as a big box, or even a pool of water. You might be wondering, "Why do we measure the volume of solid objects in cubic measurements?" Well, it's because volume is a three-dimensional quantity. It takes into account the length, width, and height of an object. Cubic measurements allow us to consider all three dimensions together, giving us a more accurate measure of the space inside an object. This is important to remember as you dive deeper into the concept of volume, eventually learning how to solve for volume. Now that we have explored units of volume, let's wrap it up. To summarize, volume is a measure of how much space an object takes up, and can be measured using the metric or customary system. Liquid volume and solid volume have their own ways of being represented. Liquid volume use measurements such as fluid ounces, cups, quarts, and gallons. Solid volume measurements include the term cubic, which relates to the length, width, and height of the volume an object has. So the next time you take a swim in a pool, think about how much volume you are observing being taken up within that space!

Units of Volume exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Units of Volume.
• Demonstrate your understanding of the units of volume.

Hints

Cubes are used to measure volume.

We can use the cubes to measure the length, width, and height.

Solution

To measure volume, we use cubes because volume is about filling space in three dimensions: length, width, and height. A cube has all three (length x width x height), making it perfect for measuring volume. We write this as ³, which means cubed.

• Match each unit of volume to the correct phrase.

Hints
• A cubic centimeter can be used to measure a tiny sugar cube, that's about a cubic centimeter.
• A cubic inch can be used to measure a small toy block.
• A cubic foot can be used to measure a storage container or box.
• A cubic meter can be used to measure a swimming pool for this size.

A cubic centimeter is the smallest unit of measure and a cubic meter is the largest.

Solution

This is a table of the different units of volume measurement and their common uses. It is important to remember that this is a partial list of measurements that can be used with volume.

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• Cubic Centimeter ($\text{cm}^3$): This unit is for small objects.
• Cubic Inch ($\text{in}^3$): This is a bit larger than the smallest unit.
• Cubic Foot ($\text{ft}^3$): This is used for large items or spaces.
• Cubic Meters ($\text{m}^3$): This is the largest unit.
• Match each object with the right unit used to measure it.

Hints
• The first image is a small amount of lemon juice.
• The second is a pitcher of water.
• The third is a gallon of milk.
• The fourth is a can of soda.

If you squeeze a lemon, it produces a small amount of juice. What is the smallest unit of measurement?

Volume of liquid is measured using metric units such as milliliters and liters, and customary units like ounces and gallons.

Solution
• The lemon produces a small amount of juice, so we measure it using milliliters.
• A jug of water is measured using liters.
• A gallon of milk is measured using gallons.
• A can of soda is measured using ounces.
• Which unit measures the object?

Hints

Look at each object and think: what is the biggest? Which unit of measurement is the largest?

Meters is the largest unit, so we measure the largest object with meters.

Solution
• A piece of a puzzle is very small, so we use centimeters.
• The blocks are bigger than the puzzle pieces, so we measure using cubic inches.
• The present is larger than the blocks but smaller than the house so we measure using cubic feet.
• The house is the largest object, so we measure using cubic meters.
• How do we measure volume?

Hints

A cubic meter ($\text{m}^3$) is a unit of volume used for larger spaces, representing a cube with each side measuring one meter.

A gram is a mass measurement not a weight. Mass is the measurement of matter an object contains while weight is the gravitational pull the earth has on an object.

Solution

• Common units include cubic centimeters, cubic inches, and cubic feet.
• There's no such thing as cubic mass, mass is used to measure the gravitational pull the earth has on an object.
Grams are a unit of mass, while cubic typically refers to volume.

• A cubic meter ($\text{cm}^3$ ) is a unit of volume used for larger spaces, representing a cube with each side measuring one meter. A cubic centimeter ($\text{cm}^3$): This unit is used for small objects.
• A cubic foot ($\text{ft}^3$ ) is a unit of volume used for large items or spaces. A cubic inch ($\text{in}^3$): This unit is used for small objects.