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Unit of Volume is the measuring unit which determines the volume or capacity of an object. A metric system of measures uses a variety of fundamental units for length, mass, and volume. The most material that a container can hold, either in terms of volume or weight, is considered it's capacity. Volume is the measure of capacity. Volume is the fundamental physical quantity. The cubic metre (m3) is the SI unit of volume. However, many other units like litre (L), cubic centimetre (cm3), fluid ounce (fl oz), pint (pt), quart (qt), gallon (gal), teaspoon (tsp), and a tablespoon (tbs) can be used to measure volume.
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Key Terms: Volume, Cubic Metre, Length, Breadth, Unit Conversion, Capacity, Mass, Litre, Gallon
What is Volume?
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Volume of an object or shape refers to how much 3-dimensional space (length, height, and breadth) it takes up. The formula to calculate the volume is given by:
| Volume = Base Area x Height |
A unit of volume is a measuring unit for volume or capacity, which is the three-dimensional extent of an object or space.
The cubic metre (m3) is the SI unit of volume.
Units and Measurements Video Lecture
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Measurement and Unit of Volume
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Volume of an object is the amount of three-dimensional space it takes up.
For example, A bowl's volume is the amount of space inside the bowl or the amount of water required to fill the bowl.
Volume can be calculated via water displacement or by taking measurements and solving the volume equation for the object.
Since volume is measured in three dimensions (length, breadth, and depth), it is stated in cubic units (3).
Examples of cubic units: cm3, m3, and cubic feet.
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SI Unit of Volume
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Depending on the three-dimensional use of the base unit for length, the metre, the cubic metre, or m3 is the derived SI unit for volume.
Volume = length x breadth x height
Units are = m x m x m = m3
There are different units for measuring large and small amounts of volume, which can be seen as follows:
| Unit of Volume | SI Unit in Cubic Metre | Litre |
|---|---|---|
| cubic kilometre | km3 | 1,000,000,000 m3 |
| hectometer cubic | hm3 | 1,000,000m3 |
| decameter cubic | dam3 | 1,000 m3 |
| cubic meter | m3 | 1 m3 |
| cubic decimetre | dm3 | 0.001 m3 |
| cubic centimetre | cm3 | 0.000001 m3 |
| cubic millimetre | mm3 | 0.000000001 m3 |
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SI Units for the Volume of a Liquid
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Volume of liquid is measured in litres in the metric system.
The unit of volume of a fluid is represented in a litre (L) = 10-centimetre cube in the metric system.
Thus,
1 litre = 10 cm3 = 1000 cubic centimetres. = 0.001 cubic metre
Read More: Dispersion through Prism
Conversion of Cubic Metres
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The m3 unit is commonly used to measure the volume of solids or liquids (fluids).
The following list will show the units used all over the world:
| Unit of measuring volume | Cubic Metre | Litre |
|---|---|---|
| 1 cubic metre | = 1 | = 1000 |
| 1 barrel | = 0.158 987 294 928 | = 158.987294928 |
| 1 cubic foot | = 0.028 316 846 592 | = 28.316864592 |
| 1 cubic decimetre | = 0.001 | = 1 |
| 1 litre | = 0.001 | = 1 |
| 1 gallon (US) | = 0.003 785 411 784 | = 3.785411784 |
| 1 pint (US) | = 0.000 473 176 473 | = 0.473176473 |
| 1 cubic inch | = 0.000 016 387 064 | = 0.016387064 |
| 1 cubic centimetre | = 0.000 001 | = 0.0010000 |
Cubic Meters to Litres
One cubic metre is exactly equivalent to one thousand litres. As a result, to convert from cubic metres to litres, we must multiply the figure by 1000 litres.
1 cubic meter = 1000 litres
1 litre = 10 cm3 = 1000 cubic centimetres. = 0.001 cubic metre
So,
1000 gallons = 1 cubic metre.
Millilitres are used to measure small volumes of liquid.
0.001 litres or 1 cubic centimetre = 1 millilitre.
Similarly,
Enormous amounts are measured in mega-litres, i.e., billions of litres.
1000 m3 (1 mega-litre) = 1 million litres
Read More: Helmholtz Equation
Converting Volume Units
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Unit conversion refers to changing a quantity's measurement from one unit to another. When a particular quantity is stated in other units, it might be expressed as a variety of values. A conversion factor is multiplied or divided by a number of steps that involve the unit conversion process.
The conversion of cubic metres into other units is tabulated below:
| Cubic Metre(m3) | Other Units |
|---|---|
| 1 | 1000 Litres |
| 1 | 35.3 cubic feet |
| 1 | 1.31 cubic yards |
| 1 | 61023.7441 cubic inches |
| 1 | 6.29 oil barrels |
| 1 | 220 imperial gallons |
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Things to Remember
- The word "unit volume" refers to the volume of a single item.
- The SI unit of volume is the cubic meter (m3).
- A unit of volume is a measuring unit for volume or capacity, which is the three-dimensional extent of an object or space.
- Volume can be calculated via water displacement or by taking measurements and solving the volume equation for the object.
- The unit of volume of a fluid is represented in a litre (L) = 10-centimetre cube in the metric system.
- Three common volume units are cubic centimetres, litres and gallons.
- Some other volume units are fluid ounce (fl oz), pint (pt), quart (qt), gallon (gal), teaspoon (tsp), tablespoon (tbs), etc.
Previous Years’ Questions
- A screw gauge has least count of 0.01 mm and there are 50 divisions … [NEET – 2020]
- Dimensions of stress are...[NEET – 2020]
- Lumen is the unit of… [UPSEE – 2019]
- A quantity z, to be estimated has a dependency on the variables… [TS EAMCET – 20219]
- A student measured the diameter of a small steel ball using… [NEET – 2018]
- A physical quantity of the dimensions of length that can be formed… [NEET – 2017]
- Planck’s constant (ℎ), speed of light in vacuum (c) and Newton”s gravitational constant… [NEET – 2016]
- Which of the following is the smallest unit… [UPSEE – 2010]
- Body weighs 22.42 g and has a measured volume of 4.7… [WBJEE – 2010]
- A student measures the distance traversed in free fall… [NEET – 2010]
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Sample Questions
Ques: The height, breadth, and length of a large tank are 5 m, 8 m, and 400 cm, respectively. A smaller tank with a volume of 12,0000 dm3 is also available. Is the volume of the larger tank greater than that of the smaller tank and by how many cubic metres? (5 Marks)
Ans: The height of the larger tank is 5 metres.
The width of the larger tank is 8 metres.
The length of the larger tank is 400 cm, or 4 metres (1 metre = 100 cm).
The larger tank has a volume of 5 x 8 x 4 = 160 m3.
The smaller tank's volume is measured in cubic decimetres. As a result, we'll start by converting this volume into cubic metres.
The smaller tank has a volume of 12000 dm3.
1000 dm3 = 1 m 3
Known: dm3 is the smaller unit and m3 is the larger unit. As a result, we'll divide to change the value from a smaller to a larger unit:
120 m3 = frac1200001000 dm3 = 12,00,00 dm3
The volumes of both tanks, allowing us to determine the number of cubic metres. The larger tank's volume is greater than the smaller tank's volume.
160 m3 minus 120 m3 equals 40 m3
As a result, the larger tank's volume is 40 m3 greater than the smaller tank's volume.
Ques: Convert 92,000 cubic centimetres to kiloliters. (5 Marks)
Ans: Convert cm3 to m3, then m3 to dm3.
1 m3 =1000000 cm3
92000 cm3 = 92000/1000000 m3
= 0.092 m3
Now convert the m3 value to dm3 value.
1000 dm3 = 1 m3
0.092 m3 = 0.092 / 1000 dm3
= 92 dm3
Because 1 dm3 equals 1 litre, 92 dm3 equals 92 litres.
Divide 92 by 1000 to convert litres to kiloliters. (Keep in mind that one kiloliter equals 1000 litres.)
92 litres = 92/1000 kiloliters.
= 0.092 kiloliters.
Ques: A water tank's length, width, and height are 5 metres, 2.5 metres, and 1.25 metres, respectively. Calculate the Water Tank's Capacity in (A) M3 (B) litre. (5 Marks)
Ans: Given,
Length (1) = 5m
Breadth (b) = 2.5 m
Height (h) = 1.25 m
(a) Water tank volume = l × b × h m3
= 5m × 2.5 m × 1.25 m
= 15.625m3
(b) Water tank volume in litre = 15.625 × 1000
= 15625 litre
Ques: In a measuring cylinder, a solid silver piece is immersed in water. The water level rises from 50 to 62 millilitres. Calculate the volume of the silver piece. (5 Marks)
Ans: Given, Initial water level v1 = 50 ml
Final water level v2 = 62 ml
Silver piece volume V = v2 – v1
= 62 ml – 50 ml
= 12 ml
As, 1 ml = 1 cm3
So, 12 ml = 12 cm3
Ques: Calculate the volume of a liquid in a dish with dimensions of 10 cm x 10 cm x 5cm. (3 Marks)
Ans: Volume of water = Length × breadth × height
= 10 cm × 10 cm × 5 cm
= 500 cm3
or 500 ml.
Ques. What is volume? (1 Mark)
Ans. The amount of three-dimensional space in a closed surface is described by the scalar concept known as volume.
Ques. Find the volume of a cube if its side length is equal to 6 cm. (2 Marks)
Ans. Given, the length of cube = 6 cm
Volume of cube = Side3
Therefore,
Volume of cube with 6 cm length = 63 (cm)3
Volume = 216 cm3
Ques. Convert 0.135 cubic meters into cubic feet. (3 Marks)
Ans. Known: 1 cubic meter = 35.3 cubic feet
Hence,
0.135 cubic meters = 0.135 × 35.3 cubic feet
0.135 m3 = 4.7655 ft3
0.135 m3 = 4.765 ft3
Therefore, 0.135 cubic meters is approximately equal to 4.765 cubic feet.
Ques. Define Mass. (1 Mark)
Ans. The amount of matter that makes up a physical body is known as its mass. The SI Unit of Mass is Kilogram (Kg)
Ques. How to convert Litres to cubic metre. (2 Marks)
Ans. The unit of volume of fluid in a litre (L) = 10-centimetre cube in the metric system.
Thus,
1 litre = 10 cm3 = 1000 cubic centimetres. = 0.001 cubic metre
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