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.

 

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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 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 2.36 hm^3 into m^3.

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.

1 hm^3 = 1000,000 m^3

2.36 hm^3 = 2.36 \cdot 1000,000 m^3

= 2,360,000 m^3

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

= 2.36  x 10 ^6 m^3

 

Example 2

Convert 15,000 mm^3 into cm^3.

Solution

For our ease, first, we will convert mm^3 to m^3, and then m^3 to cm^3. Since mm^3 is a smaller unit and m^3 is a bigger unit, therefore, we will use the arithmetic operation of division for conversion.

1 m^3 = 1000000000 mm^3

15,000 mm^3 = \frac{15000}{1000000000}

=0.000015 m^3

Now, we have the value of m^3, so we will convert it into the cm^3. Cubic meters is a bigger unit than cubic centimeters, hence we will multiply for this conversion:

1 m ^3 = 1000000 cm^3

0.000015 m^3 = 0.000015 \cdot 1000000 cm^3

= 15 cm^3

 

Example 3

Convert 18 m^3 to dam^3.

Solution

dam^3 is a bigger unit and m^3 is a smaller unit, therefore, in this problem we will divide to convert the value from a smaller to a bigger unit.

1 dam^3 = 1000 m^3

18 m^3 = \frac{18}{1000} dam^3

= 0.018 dam^3

 

Example 4

Convert 18,00 dm^3 into cm^3.

Solution

For our ease, first, we will convert dm^3 to m^3, and then m^3 to cm^3. Since dm^3 is a smaller unit and m^3 is a bigger unit, therefore, we will use the arithmetic operation of division for conversion.

1 m^3 = 1000 dm^3

18,00 dm^3 = \frac{1800}{1000} m^3

=1.8 m^3

Now, we have the value of m^3, so we will convert it into the cm^3. Cubic meters is a bigger unit than cubic centimeters, hence we will multiply for this conversion:

1 m ^3 = 1000000 cm^3

1.8 m^3 = 1.8 \cdot 1000000 cm^3

= 1800,000 cm^3

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

= 1.8 x 10 ^6 cm^3

 

Example 5

Convert 85 dam^3 into dm^3.

Solution

For our ease, first, we will convert dam^3 to m^3, and then m^3 to dm^3. Since dam^3 is a bigger unit and m^3 is a smaller unit, therefore, we will use the arithmetic operation of multiplication for conversion.

1 dam^3 = 1000 m^3

85 dam^3 = 85 \cdot 1000 m^3

=85000 m^3

Now, we have the value of m^3, so we will convert it into the dm^3. Cubic meters is a bigger unit than cubic decimeters, hence we will multiply for this conversion:

1 m ^3 = 1000 dm^3

85000 m^3 = 85,000 x 1000 dm^3

= 85,000,000 dm^3

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

= 8.5 x 10 ^7 dm^3

 

Example 6

Convert 20 m^3 into liters.

Solution

We know that 1 cubic decimeters is equal to 1 liter. In this example, we are given the value in m^3. Hence, we will  convert m^3 to dm^3 to give the final value in liters.

1 m^3 = 1000 dm^3

20 m^3 = 20 \cdot 1000 dm^3

= 20,000 dm^3

Hence, 20 m^3 equals to 20,000 dm^3.

 

Example 7

Convert 92,000 cm^3 to kiloliters.

Solution

First, we will convert cm^3 to m^3, and then m^3 to dm^3.

1 m ^3 = 1000000 cm ^3

92000 cm^3 = \frac{92000}{1000000} m^3

= 0.092 m^3

Now, we will convert the value in m^3 to dm^3

1 m^3 = 1000 dm^3

0.092 m^3 = 0.092 \cdot 1000 dm^3

= 92 dm^3

Since, 1 dm ^3 = 1 liter, hence 92 dm^3 is equal to 92 liters. To convert the liters into kiloliters, we will divide 92 by 1000. (Remember 1 kiloliter = 1000 liters).

92 liters = \frac{92}{1000} 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 dm^3. 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 m^3.

 

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 dm^3

1 m ^3 = 1000 dm^3

Remember that dm^3 is a smaller unit and m^3 is a bigger unit. Hence, we will divide to convert the value with smaller unit to a bigger unit:

12,00,00 dm^3 = \frac{120000}{1000} m^3

= 120 m^3

 

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.

= 160 m^3 - 120 m^3

= 40 m^3

Hence, the volume of the bigger tank is 40 m^3 greater than the volume of the smaller tank.

 

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Rafia Shabbir