Volume and Capacity: Mensuration, Units & Examples

Volume and Capacity: We confront various three-dimensional objects that occupy a specified volume in our daily lives. The volume of a substance indicates the total amount of space that it covers. In other words, when we measure the space region occupied by a solid object, it is stated as volume. In contrast, capacity describes the quantity of something that a container holds. In brief, the capacity is described as the container’s volume. As there are many similarities between these two, the volume is generally confused with the capacity. However, there are a few but some important differences between volume and capacity. Let us learn about volume and capacity in detail.

Volume

Let us learn the meaning by volume in detail in this part. In mathematics, the term volume is described as the amount which is occupied by a three-dimensional object. It is nothing but space, which is taken up by a substance that can be solid, liquid or gas. It measures the whole size of the given three-dimensional figure.

We have specific formulas to find the volume of different three-dimensional shapes like cube, cuboid, cylinder, cone, sphere, etc.

Volume: Units

Generally, volume is measured in cubic units, cubic meters, cubic centimetres, etc. Further, based on what is the shape of the object, its volume is likely to change. The volume of an object gives you an insight into how much space is occupied by the object.

For example, if the measurements are given in \({\rm{m}},\) then the volume will be in \({{\text{m}}^3}{{\text{m}}^3}\) is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are \({\text{c}}{{\text{m}}^3}{\text{m}}{{\text{m}}^3},{\text{inc}}{{\text{h}}^3},\) etc.

Volume: Formulas

There are some specific formulas by which we can find the volume of different shapes. Let us learn about some very familiar three-dimensional shapes.
The formula of volume of the cuboid with length \(l,\) breadth \(b,\) and height \(h\) is given by \(V = \left({l \times b \times h} \right){\text{cubic}}\,{\text{units}}\)

The formula of volume of a cube of side length a is given by
\(V = {a^3}{\text{cubic}}\,{\text{units}}\)

The formula of volume of a cylinder with radius \(r\) and height \(h\) is,
\(V = \pi {r^2}h\,{\text{cubic}}\,{\text{units}}\)

The formula of the volume of a cone of radius \(r\) and height \(h\) is, \(V = \frac{1}{3}\pi {r^2}h\,{\text{cubic}}\,{\text{units}}\)

The formula of the volume of a sphere of radius \(r,V = \frac{4}{3}\pi {r^3}\,{\text{cubic}}\,{\text{units}}\)

Capacity

Let us now study capacity and the measurement of capacity. The term capacity refers to the ability of the hollow object to hold a substance or a matter. A measure determines the amount of space available in a vessel that can be loaded with the matter. In other words, the total amount of matter that can be contained in the given container or vessel is called the capacity of the container.

Capacity: Units

You might have noticed several times that when you fill up any hollow object with liquid or gas, it takes the shape of that object. Hence, the maximum amount of matter that the container can hold is known as its capacity. Capacity is measured in metric units such as \({\text{litres}},{\text{gallons}},{\text{pint}},{\text{quarts,}}\) etc.

Units of Capacity for Liquid

To measure the capacity of liquids, we use litres.
We know,
\(1\,{\text{litre}} = 1000\,{\text{c}}{{\text{m}}^3}\)
\(1000\,{\text{c}}{{\text{m}}^3} = \frac{{1000}}{{100 \times 100 \times 100}}{{\text{m}}^3} = 0.001\,{{\text{m}}^3}\,0.001\,{{\text{m}}^3} = 1\,{\text{litre}}\)
Hence, \(1\,{{\text{m}}^3} = 1000\,{\text{litres}}\)

Customary Units of Capacity for Liquid

The American metric system is also called the United States Customary Units (USCS), follows five customary units to measure the capacity.

The American metric system is also called the United States Customary Units (USCS), follows five customary units to measure the capacity.

This chart represents that \(1\,{\text{gallon}} = 4\,{\text{quarts}} = 8\,{\text{pints}} = 16\,{\text{cups}} = 48\,{\text{Fluid}}\,{\text{ounce}}\)

Volume and Capacity: Examples

Let us look at the instances of volume and capacity. Consider a beaker that is full of a liquid. Therefore, volume implies the space taken up by the beaker and water, while its capacity refers to the quantity of liquid required to fill it.

In the left-side image, the beaker is full of liquid which indicates its capacity. It indicates the highest amount of liquid the beaker can contain.
In the right-side image, there is \(60\,{\text{ml}}\) liquid in the beaker. So, the volume of the liquid in the beaker is \(60\,{\text{ml}}.\)

Difference Between Volume and Capacity

Solved Examples – Volume and Capacity

Q.1. Find the volume of a cylindrical shape oil container that has a height of \(8\,{\text{cm}}\) and diameter of \(12\,{\text{cm}}\) considering \(\pi = 3.14.\)
Ans: Given,
Diameter of the container \( = 12\,{\text{cm}}\)
Thus, the radius of the container \( = \frac{{12}}{2}\,{\text{cm}}\,{\text{=6}}\,{\text{cm}}\)
Height of the container \(\,{\text{=8}}\,{\text{cm}}\)
The formula of the volume of a cylinder \(\,{\text{=}}\pi {r^2}h\,{\text{cubic}}\,{\text{units}}.\)
Therefore, the volume of the given container \(\,{\text{=}}\pi {\left( 6 \right)^2} \times 8\,{\text{c}}{{\text{m}}^3}\)
Volume \(\,{\text{=3}}{\text{.14}} \times {\left( 6 \right)^2} \times 8\, = 904.32{\text{c}}{{\text{m}}^3}\)

Q.2. Convert \(\,5\,{{\text{m}}^3}\) into litres.
Ans: We know,
\(1\,{\text{litre}} = 1000\,{\text{c}}{{\text{m}}^3}\)
\(1000\,{\text{c}}{{\text{m}}^3} = \frac{{1000}}{{100 \times 100 \times 100}}{{\text{m}}^3} = 0.001\,{{\text{m}}^3}\)
\( \Rightarrow 0.001\,{{\text{m}}^3} = 1\,{\text{litre}}\)
\( \Rightarrow 1\,{{\text{m}}^3} = 1000\,{\text{litres}}{\text{.}}\)
Hence, \(5\,{{\text{m}}^3} = 5000\,{\text{litres}}\)

Q.3. Find the capacity and the volume of a cylinder whose radius is \(5\,{\text{cm}}\) and height is \(21\,{\text{cm}}.\)
Ans: Given, \(r = 5\,{\text{cm}}\) and \(h = 21\,{\text{cm}}\)
We know that,
The volume of a cylinder \(\left( V \right) = \pi {r^2}h\)
\( = \frac{{22}}{7} \times {\left( 5 \right)^2} \times 21\)
\( = 22 \times 25 \times 3 = 1650\,{\text{c}}{{\text{m}}^3}\)
Therefore, the capacity of the cylinder \( = \frac{{1650}}{{1000}}{\text{litres}}\left({1000\,{\text{c}}{{\text{m}}^3} = 1\,{\text{litres}}} \right)\)
\( = 1.65\,{\text{litres}}\)
Hence,the capacity of the cylinder is \( = 1.65\,{\text{litres}},\) and the volume is \(1650\,{\text{c}}{{\text{m}}^3}.\)

Q.4. Harsha made \(12\,{\text{quarts}}\) of mango juice. He divided it into an equal number of cups. How many cups would he have used?
Ans: The conversion chart of the capacity is given below.

Q.5. Find the capacity of the cubical tank whose each edge is \(5\,{\text{m}}{\text{.}}\)
Ans: From the given edge \(a = 5\,{\text{m}}{\text{.}}\)
We know that the formula of the volume of a cube is \({a^3}{\text{.}}\)
\(V ={a^3}\,{\text{cubic}}\,{\text{units}}\)
\( \Rightarrow V = {5^3}\)
\(\Rightarrow V = 125\,{{\text{m}}^3}\)
To find its capacity, we need to convert the \({{\text{m}}^3}\) into litres as we measure the capacity in litres.
We know,
\({\text{1}}\,{{\text{m}}^3} = 1000\,{\text{litres}}.\)
Therefore, the capacity of the tank is \({\text{125}}\,{{\text{m}}^3} = 125000\,{\text{litres}}\)

Summary

In this article, we studied the definitions of volume and capacity, units of volume, and capacity. We discussed that we measure the space region occupied by a solid object. It is stated as volume. In contrast, capacity describes the quantity of something that a container holds. We learned the difference between volume and capacity and solved some examples related to volume and capacity.

Learn About Volume of Solids

Frequently Asked Question (FAQs)

Frequently asked questions related to volume and capacity is listed as follows:

Q. What are volume and capacity?
Ans: In mathematics, the term volume is described as the amount which is occupied by a three-dimensional object. It measures the whole size of the given three-dimensional figure. The term capacity refers to the ability of the hollow object to hold a substance or a matter. A measure determines the amount of space available in a vessel that can be loaded with the matter.

Q. Write two major differences between capacity and volume?
Ans:

Q. Give one example of volume and capacity
Ans: Let us take an example of volume and capacity. Consider a water tank that is filled with water. Therefore, volume implies the space occupied by the tank and water, while its capacity indicates the quantity of water required to fill it.

Q. Are volume and capacity the same formula?
Ans: Calculating the capacity of some containers is almost the same as calculating the volume of the container. To calculate the capacity of a container, we need to find the volume of the container.

Q. What are the uses of litres and millilitres?
Ans: Litres are used in measuring the capacity of milk, kerosene, cooking oils, petrol, etc. We use millilitres to measure the capacity of chemicals, medicinal liquids like syrup, liquid antiseptic medicine, etc. A small amount of cooking oil, ketchup etc., are measured in millilitres.

We hope this detailed article on volume and capacity helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!