Units of volume 
Name: ______________________________________ Subject: _______________________ Date: _______
Write on the right side what is missing.
1. The cubic meter
The cubic meter is the volume of a cube with edges one meter in length. Its symbol is: m^{3}.
2. Multiples of the cubic meter
These are:
1 cubic decameter is equal to 1 000 cubic meters: 1 dam^{3} = 1 000 m^{3} .
1 cubic hectometer is equal to 1 000 000 cubic meters: 1 hm^{3} =
1 000 000 m^{3}.
1 cubic kilometer is equal to 1 000 000 000 cubic meters: 1 km^{3} =
1 000 000 000
m^{3}.
1 cubic myriameter is equal to 1 000 000 000 000 cubic meters: 1
mam^{3} = 1 000 000 000 000 m^{3}.
The units of volume increase and decrease from 1000 to 1000.
The superior unit is 1000 more than the lower.
It answers these questions in: m^{3}:
3 km^{3} = 

7 dam^{3} = 

8 hm^{3} = 
3.  Submultiples of the cubic meter
The picture shows a cube that has 1dm per side. Its volume is the unit called cubic decimeter (dm^{3}). It can be divided into 10 layers of 100 cm^{3}. Then 1 dm^{3} = 1000 cm^{3}. Each cm^{3} can be divided into 1000 parts or mm^{3}..
The submultiples are these:
1 cubic decimeter is equal to 0.001 cubic meter: 1 dm^{3} = 0,001 m^{3}. 1 m^{3} tiene
1 000 dm^{3}.
1 cubic centimeter is equal to 0.000 001 cubic meter: 1 cm^{3} =
0,000 001 m^{3}. El m^{3} is 1 000 000 cm^{3}.
1 cubic millimeter = 0.000 000 001cubic meter: 1 mm^{3} =
0,000 000 001
m^{3}. El m^{3} is 1 000 000 000 m^{3}.
The units of volume increase and decrease from 1000 to 1000.
The lower unit is 1000 less than the superior.
It answers these questions in m^{3}:
7 dm^{3} = 

3 137 cm^{3} = 

8 385 dm^{3} = 
4. Conversion of unit
Each unit of volume is 1000 times greater than the immediate lower and 1000 times less than the immediate superior.
To convert from dam^{3} to
m^{3}
we multiply by 1000 or we move the decimal point three places to the right.
Examples: 5 dam^{3} = 5000 m^{3}; 25,324 hm^{3} =
25 324 dam^{3} = 25 324 000 m^{3}.
To convert from m^{3} to
dam^{3}
we divide by 1000 or we move the decimal point three places to the left.
Examples: 2 m^{3} = 0,002 dam^{3}; 1 468 m^{3} =
1,468 dam^{3} = 0,001 468 hm^{3} = 0,000 001 468 km^{3}.
It answers these questions in m^{3}:
7,32 dam^{3} = 

18,457 hm^{3} = 

0,0073 km^{3}= 
5. Converting from complex to noncomplex
To convert from complex of volume to noncomplex of lower order, we write the numbers of successive orders, reserving two places for each order and placing zeros in the empty places.
Example: 3 mam^{3}, 735 hm^{3} y 5 cm^{3} can be written as: 3 000 735 000 000, 000 005 m^{3}
It answers these questions in m_{3}
3 km^{3}, 741 dam^{3} y 31 m^{3} = 

83 hm^{3} y 798 dm^{3} = 

7 dam^{3}, 8 dm^{3} y 3 cm^{2} = 
6. Converting from noncomplex ( 12 500 m^{3} ) to complex ( 12 dam^{3} y 500 m^{3} ).
To convert from noncomplex of volume to complex, we separate the numbers in groups of three, from the decimal point, putting the corresponding names to their orders. The number of the units is the same order as the incomplete.
For example: 4 023 715,67 cm^{3}, can be written as: 4 m^{3}, 23 dm^{3} and 715 cm^{3} y 670 mm^{3}.
Examples:
32 000 026 m^{3} = 32 hm^{3} and 26 m^{3}
17,028 m^{3} = 17 m^{3} and 28 dm^{3}.
5,6 mam^{3} = 5 mam^{3} and 600 km^{3}.
7. Problems
To find the volume of a cube, we multiply the length by the width by the height.
Do these problems on paper and write the solution:
1. A cube is 4.5 cm of edge. How many cm^{3} does the volume is? 

2. A die is 2 cm of edge. What is its volume in cm^{3}? 

3. The cubic pieces of soap of 5 cm edge has been send in cubic boxes of 60 cm edge . How many pieces can the box contain? 

4. In a box of 0.696 dam^{3}, how many cubes of 12 m^{3} fit? 

5. There are 1.23 m^{3} of wine in a barrel. How many bottles of 0.75 liters can we fill? (1 liter=1 dm^{3}) 

6. A jar that has 0.4 m^{3} of oil has cost 800 euros. How much money do we have to pay for a liter? 

7. A vintner buys 3 m^{3}. First he sold 128 liters and the rest is distributed in 8 equal barrels. How many dm^{3} did he pour in each barrel? 

8. A boat transports 75 dam^{3} of wine and we want pack it in barrels of 1.2 m^{3}. How many barrels will we need? 

9. A box is 3.5 m on each side. How many liters of water will fit in the box? 

10. A candy has a volume of 1.3 cm^{3}. How many candies fit in a box of 0.4498 dm^{3}? 
 Educational applications 
Matemáticas 
In Spanish  Interactive
®Arturo Ramo García.Record of intellectual property of Teruel (Spain)
No 141, of 29IX1999
Plaza Playa de Aro, 3, 1º DO 44002TERUEL