# Lesson Video: Converting Capacity - Metric Units Mathematics

In this video, we will learn how to convert cubic meters, cubic decimeters, cubic centimeters, liters and milliliters, and solve word problems.

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### Video Transcript

In this video, we will learn how to convert metric units of capacity. These will include cubic centimeters, cubic decimeters, cubic meters, and milliliters and liters. We will begin by looking at some key definitions and conversions.

Your teacher might well have used the words volume and capacity. Whilst these are often interchangeable in mathematical questions, there are some subtle differences between them. Firstly, volume is the amount of space taken up by an object, while capacity is the measure of an object’s ability to hold a substance like a solid, a liquid, or a gas. We tend to get asked questions about the volume of a three-dimensional shape, such as a cuboid or a cylinder. However, we would be asked to calculate the capacity of a fish tank. This is because we would be looking to calculate the amount of water the fish tank could hold.

Volume is measured in cubic units, such as centimeters cubed, decimeters cubed, or meters cubed, whereas capacity can be measured in units such as gallons, pints, liters, and milliliters. In this video, we will deal with liters and milliliters as these are the metric units. We will now look at some key conversions between the units.

When dealing with volume, we firstly need to consider meters, decimeters, and centimeters. The prefix deci- denotes a factor of one-tenth and comes from the Latin “decimus” meaning tenth. A decimeter is therefore one-tenth of a meter. In the same way, centi- comes from the Latin “centum” and one centimeter is one-hundredth of a meter. These prefixes mean that there are 100 centimeters in one meter and 10 centimeters in one decimeter. We can see how this corresponds to the volume conversions by firstly considering a one-centimeter cube. This has a volume of one cubic centimeter.

A one-decimeter cube will have dimensions 10 centimeters by 10 centimeters by 10 centimeters. Multiplying 10 by 10 by 10 gives us 1000. Therefore, one cubic decimeter is equal to 1000 cubic centimeters. We could repeat this process to convert from cubic centimeters to cubic meters or cubic decimeters to cubic meters. There are three conversions we need to remember. 1000 cubic centimeters is equal to one cubic decimeter. 1000 cubic decimeters is equal to one cubic meter. And finally, 1000000 cubic centimeters is equal to one cubic meter. We can therefore convert from cubic centimeters to cubic decimeters by dividing by 1000 and from cubic decimeters to cubic meters by dividing by 1000.

If we need to convert in the opposite direction, we need to multiply by 1000. When dealing with capacity, 1000 milliliters is equal to one liter. This is because the prefix milli- means one-thousandth. Once again, to convert from milliliters to liters, we would divide by 1000 and, from liters to milliliters, multiply by 1000. It is also important to know that we can convert from volume to capacity using the fact that one cubic centimeter is equal to one milliliter. This in turn leads to the fact that one cubic decimeter is equal to one liter, and one cubic meter is equal to 1000 liters. We will now use these conversions to solve some problems involving volume and capacity.

Write in cubic decimeters 5625 cubic centimeters.

We begin by recalling that the prefix deci- means one-tenth and centi- means one-hundredth. This means that a decimeter is one-tenth of a meter and a centimeter is one-hundredth of a meter. There are 10 centimeters in one decimeter. By considering the two identical cubes, one in decimeters and one in centimeters, we can see that one cubic decimeter is equal to 1000 cubic centimeters. This means that, in order to convert from cubic centimeters to cubic decimeters, we need to divide by 1000. The calculation required in this question is 5625 divided by 1000. When dividing by 1000, we move all our digits three places to the right. 5625 cubic centimeters in cubic decimeters is 5.625.

Our next question involves ordering capacities and volumes.

Arrange in ascending order: 1800 cubic centimeters, 6.8 cubic decimeters, 1.3 cubic decimeters, and 1100 cubic centimeters.

As we are asked to arrange the values in ascending order, we need to do so from least to greatest. In order to do this, we need to ensure that our units are the same. Currently, we have two in cubic centimeters and two in cubic decimeters. We recall that there are 1000 cubic centimeters in one cubic decimeter. This means that, in order to convert from cubic centimeters to cubic decimeters, we need to divide by 1000. To convert from cubic decimeters to cubic centimeters, we multiply by 1000. This is the method we will use in this question. We will convert 6.8 and 1.3 cubic decimeters into cubic centimeters.

When multiplying by 1000, we move all the digits three places to the left. So 6.8 multiplied by 1000 is 6800. In the same way, 1.3 multiplied by 1000 is 1300. We now have all four values in cubic centimeters. The smallest or least value is 1100 cubic centimeters. The next smallest value was 1300 cubic centimeters, which is the same as 1.3 cubic decimeters. Next, we have 1800 cubic centimeters. And finally, the largest or greatest value is 6800 cubic centimeters or 6.8 cubic decimeters. In order to write any set of values in ascending or descending order, we firstly need to ensure that all the units are the same.

Our next question involves conversion and an addition calculation.

Write the answer in cubic centimeters: 4.3 cubic decimeters plus 5950 cubic centimeters.

We immediately notice in this question that our two values have different units. As we’ve been asked to write the answer in cubic centimeters, we need to convert our first value from cubic decimeters to cubic centimeters. There are 1000 cubic centimeters in one cubic decimeter. This means that, in order to convert from cubic centimeters to cubic decimeters, we would divide by 1000. To convert the other way as we need to in this case, we need to multiply by 1000. 4.3 multiplied by 1000 is 4300. So 4.3 cubic decimeters is the same as 4300 cubic centimeters. We now need to add 4300 and 5950. This is equal to 10250. The answer to the question 4.3 cubic decimeters plus 5950 cubic centimeters in cubic centimeters is 10250. We could convert this answer into cubic decimeters by dividing by 1000. This would give us an answer of 10.25 cubic decimeters.

We will now move on to look at some questions involving milliliters and liters.

If five drops of water fill up a volume of five milliliters, then how many drops would fill up a volume of seven liters?

We’re told in the question that five drops of water are equal to five milliliters. This means that one drop would be equal to one milliliter. We need to calculate the number of drops in seven liters. The prefix milli- means one-thousandth. So a milliliter is one-thousandth of a liter. We can therefore use the calculation that 1000 milliliters is equal to one liter. Multiplying both sides of this by seven gives us 7000 milliliters is equal to seven liters. We can therefore conclude that as five drops of water filled up a volume of five milliliters, 7000 drops of water will fill up a volume of seven liters.

If the capacity of a tin is 42.4 liters, what is its volume in cubic decimeters?

In order to answer this question, we need to recall some of our conversions. The prefixes deci-, centi-, and milli- mean one-tenth, one-hundredth, and one-thousandth, respectively. This means that a decimeter is one-tenth of a meter. A centimeter is one-hundredth of a meter. And a milliliter is one-thousandth of a liter. As there are 10 centimeters in one decimeter, we can calculate the number of cubic centimeters in one cubic decimeter by cubing both sides. 10 cubed is equal to 1000, so there are 1000 cubic centimeters in one cubic decimeter.

We know from the prefix milli- that there are 1000 milliliters in one liter. We now need to recall how we can convert from units of capacity to units of volume. One milliliter of capacity is equal to one cubic centimeter of volume. This means that one liter of capacity must be equal to one cubic decimeter of volume. As the ratio of cubic decimeters to liters is one to one, then 42.4 liters will be equal to 42.4 cubic decimeters.

We will now summarize the key points from this video. It is important to remember that the words volume and capacity are often interchangeable in exam questions. It is important to note, though, that volume is the amount of space taken by an object, whereas capacity is an object’s ability to hold a substance such as a solid, liquid, or gas. Volume can be measured in cubic centimeters, cubic decimeters, and cubic meters. Capacity, on the other hand, can be measured in the metric units of milliliters or liters. The prefixes centi-, deci-, and milli- can be used to help us work out our conversions. A centimeter is one-hundredth of a meter, a decimeter is one-tenth of a meter, and a milliliter is one-thousandth of a liter.

As our units for volume were cubic units, we have the following conversions. 1000 cubic centimeters is equal to one cubic decimeter. We also have 1000 cubic decimeters is equal to one cubic meter. Combining these two conversions tells us that there are 1000000 cubic centimeters in one cubic meter. When dealing with capacity, there are 1000 milliliters in one liter. When converting between units of volume and units of capacity, we can use the fact that one cubic centimeter of volume is the same as one milliliter of capacity. This in turn leads us to the fact that one cubic decimeter is equal to one liter. There are 1000 liters in one cubic meter.

Recalling these conversions or remembering how to calculate them allows us to convert between different units by multiplying and dividing by 1000. These are some of the key points to remember when dealing with metric units of volume and capacity.