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In this article, you will learn units of volume, the relationship between units of volume, capacity, and mass, and how to convert one unit of volume to another. Before proceeding to discuss the units of volume, first, let us see what is meant by volume.

## What is Volume?

The volume is defined as:

"The amount of space occupied by any 3-dimensional object"

### Volume Formula

To calculate the volume, we use the following formula:

Volume = Length x Width x Height

The volume is always given in cubic units because three dimensions, length, width, and height are involved in it. Consider the following example:

**The length of a water tank is 7 feet, height 5 feet, and width 2 feet. What is the volume of the water tank?**

To compute the volume, we will put the values of length, width, and height in the following formula:

Volume = Length x Width x Height

= 7 x 5 x 2

= 70 cubic feet

In the next section, we will see what is the SI and other units of volume under the metric system.

## SI Unit of Volume

The fundamental unit for measuring volume is the **cubic meter**.

There are also other units for measuring large and small quantities of volume.

cubic kilometer | km³ | 1,000,000,000 m³ |

hectometer cubic | hm³ | 1,000,000m³ |

decameter cubic | dam³ | 1,000 m³ |

cubic meter | m³ | 1 m³ |

cubic decimeter | dm³ | 0.001 m³ |

cubic centimeter | cm³ | 0.000001 m³ |

cubic millimeter | mm³ | 0.000000001 m³ |

Note that each unit is 1,000 times larger than the previous. The problem of converting units to other units involves multiplying or dividing the unit by one followed by as many trios of zeros as there are places between them.

## Relationship between Units of Capacity, Volume, and Mass

There is a direct relationship between volume and capacity. 1 liter is the capacity equals a volume of 1 dm³.

There is also a relationship between volume and the mass of water. 1 g equals 1 cm³ of pure water at 4° C.

Capacity | Volume | Mass (of water) |
---|---|---|

1 kl | 1 m³ | 1 t |

1 l | 1 dm³ | 1 kg |

1 ml | 1 cm³ | 1 g |

In the next section, we will solve some problems in which we will convert one unit of volume into another.

## Example 1

Convert into .

### Solution

In this case, multiply (because the hm³ is greater than the m³) the unit by one followed by six zeros, since there are two places between both units.

We can also write the above answer in scientific notation like this:

= 2.36 x

## Example 2

Convert into .

### Solution

For our ease, first, we will convert to , and then to . Since is a smaller unit and is a bigger unit, therefore, we will use the arithmetic operation of division for conversion.

Now, we have the value of , so we will convert it into the . Cubic meters is a bigger unit than cubic centimeters, hence we will multiply for this conversion:

## Example 3

Convert to .

### Solution

is a bigger unit and is a smaller unit, therefore, in this problem we will divide to convert the value from a smaller to a bigger unit.

## Example 4

Convert into .

### Solution

For our ease, first, we will convert to , and then to . Since is a smaller unit and is a bigger unit, therefore, we will use the arithmetic operation of division for conversion.

Now, we have the value of , so we will convert it into the . Cubic meters is a bigger unit than cubic centimeters, hence we will multiply for this conversion:

We can also write the final answer in scientific notation like this:

= 1.8 x

## Example 5

Convert into .

### Solution

For our ease, first, we will convert to , and then to . Since is a bigger unit and is a smaller unit, therefore, we will use the arithmetic operation of multiplication for conversion.

Now, we have the value of , so we will convert it into the . Cubic meters is a bigger unit than cubic decimeters, hence we will multiply for this conversion:

We can also write the final answer in scientific notation like this:

= 8.5 x

## Example 6

Convert into liters.

### Solution

We know that 1 cubic decimeters is equal to 1 liter. In this example, we are given the value in . Hence, we will convert to to give the final value in liters.

=

Hence, equals to .

## Example 7

Convert 92,000 to kiloliters.

### Solution

First, we will convert to , and then to .

Now, we will convert the value in to

=

Since, , hence is equal to 92 liters. To convert the liters into kiloliters, we will divide 92 by 1000. (Remember 1 kiloliter = 1000 liters).

92 liters = kiloliters

= 0.092 kiloliters

## Example 8

The height, width, and length of the bigger tank are 5 m, 8 m, and 400 cm respectively. There is another smaller tank that has a volume of 12,0000 . By how many cubic meters, is the volume of the bigger tank more than the smaller tank?

### Solution

In this problem, we are not given the volume of the bigger tank. Instead, we are given the measurements of three dimensions of the tank.

Height of the bigger tank = 5 meters

Width of the bigger tank = 8 meters

Length of the bigger tank = 400 cm = 4 m (1 m = 100 cm)

Volume of the bigger tank = 5 x 8 x 4 = 160 .

The volume of the smaller tank is given in cubic decimeters. So, we will convert this volume into cubic meters first.

Volume of the smaller tank = 12000

Remember that is a smaller unit and is a bigger unit. Hence, we will divide to convert the value with smaller unit to a bigger unit:

=

Now, we have the volumes of both the tanks, so we can easily calculate number of cubic meters the volume of the bigger tank is greater than the volume of the smaller tank.

=

=

Hence, the volume of the bigger tank is greater than the volume of the smaller tank.

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