Units and Dimensions
When we look closely at the notions of dimensions and units, we can see that they have a lot of discrepancies. The dimension is the measuring of a physical quantity without taking into account numerical values. A unit, on the other hand, can be defined as a means of assigning a measurement or number to a specific dimension. Let's have a look at an illustration. Here, length has a dimension, however, the length measurements can be stated in feet (ft) or metres (m).
If we analyze the concepts of dimensions and units deeply, we will find that there are many differences between them. The measurement of a physical quantity without considering the numerical values is known as the dimension. But, in the case of a unit, it can be expressed as a method to allot a measurement or number to a particular dimension. Let us analyze an illustration. Here, length has a dimension, but the measurements of the length can be expressed in the units of feet (ft) or meters (m).
In our daily usage, we find three primary unit systems.
The International System of Units (SI units),
The British Gravitational System of Units (BG Units),
The English Engineering System of Units (Also known as English units).
These three units are used for multiple purposes of measurements and are always helpful to evaluate the precise dimension of objects.
Dimensional Formula of Volume
The dimensional formula of volume can be written as:
[M° L³ T°]
Here,
Mass = M
Length = L
Time = T
Dimension of Volume
We can define ‘Volume’ as the amount of space surrounded by a closed surface in a three-dimensional structure. We can derive an example such as the substances like solid or liquid or gas, or plasma that occupy a certain space.
Mathematically, the volume is regularly measured in the SI unit known as the cubic meter. We can consider the volume of a container as the capacity or amount that it can hold all total. Such as the quantity of fluid or gas, or liquid that the container can hold. However, the volume cannot be specified for the amount of space that the container displaces itself.
The shapes that possess a three-dimensional structure are recognized to have volume, mathematically. There is a simple illustration for volume as it can be represented for the space required for certain shapes such as straight-edged, regular, and circular shapes. These shapes can be identified effortlessly by using arithmetic formulas.
Also, we can calculate the volumes of solids that do not have a commonly known regular shape. It can be done by the integral calculus for any shape if there is a formula for the boundary of the shape.
Volume Dimensional Formula
We know that, Length x Breadth x Height = Volume
Volume can be written as,
L x L x L = L³ = Volume
So, [M° L³ T°] = Dimensional formula of volume
m³ = SI unit of Volume
What is the Dimensional Formula of Volume?
For a three-dimensional structure, the volume indicates the total space occupied by the same structure.
Cubic units = Measurement of the Volume
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
If we calculate the volume of the above picture
1 unit × 1 unit × 1 unit = The volume of a unit cube = 1 unit³
unit³ is considered as one cubic unit.
In the following figure, length, breadth, and height are given for the cube.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
So, 1 cm × 1 cm × 1 cm = The volume of cube with sides
V = 1 cm × 1 cm × 1 cm
= 1 cm³
cm³ is considered as one cubic centimeter.
Some significant units of conversion for volume are:
1,000 mm³ = 1cm³
1,000, 000 cm³= 1 m³
[M° L³ T°] = The Dimensional Formula of Volume
How to Calculate Volume From Dimensions?
Length × breadth × height = Volume (V) ------- (1)
[M° L¹ T°] = The dimensional formula of length ------ (2)
If we substitute the equation (2) in equation (1) we will get,
Volume = Length × breadth × height
V = [M° L¹ T°] × [M° L¹ T°] × [M° L¹ T°] = [M° L³ T°]
So, we conclude that dimensionally [M° L³ T°] is represented for the volume.
Solved Examples of Volume
Q1. Calculate the Volume of a Cube of Length 6 cm.
Ans: According to the question,
Side of the cube = a = 5 cm
We know that,
The volume of a cube, V = a³
V = (6)³ cm³
∴ V = 216 cm³
Q2. Calculate the Volume of a Cube Having Side 8.2 cm.
Ans: According to question,
Side of the cube = a = 8.2 cm
We know that,
The volume of a Cube, V = a³
V = (8.2)³ cm3
∴ V = 551.37 cm³
Q3. Given the Volume of a Cube is 729 cm3, then What will be the Value of the Side of that Cube?
Ans: According to the question,
Volume of a cube, V = 729 cm³
We know that,
(side)³ or (length)³ = V
So, (side)³ = 729 =
729cm³ −−−−−− \[\sqrt[3]{729cm^{3}}\] = 9cm
We conclude that the edge of the cube is 9 cm.
Q4. What will be the Volume of the Cuboid if its Length, Breadth, and Height are 15cm, 20 cm, 25 cm Respectively?
Ans: According to the question,
Length of the cuboid = 15 cm
Breadth of the cuboid = 20 cm
Height of the cuboid = 25 cm
We know that,
V= volume of the cuboid = length × breadth × height
∴ V = (15 × 20 × 25) cm³ = 7500 cm³
Conclusion
The measure of a physical quantity without considering the numerical values is known as the dimension. A unit, on the other hand, can be defined as a means of assigning a measurement or number to a certain dimension. Here, length has a dimension, however, the length measurements can be stated in feet (ft) or metres (m).
FAQs on Dimensions of Volume
1. Can you demonstrate if mL stands for volume or mass?
We're all aware that the gram is a unit of mass. The vast property of a substance is its mass. We know that a substance's amount is determined by its comprehensive qualities. Volume is likewise a broad attribute in this case. Litres (L), millilitres (mL), and cubic centimetres (cm3) are the units of measurement. So, mL stands for millilitres, and 1 mL equals one gram (mass).
Understand the difference between gram and mass.
Grams are a unit of mass or a measure of how much something weighs. Crushing a thing to make it smaller and denser has no effect on its mass. A raisin, a paper clip, and a sugar packet all weigh around one gram.
Understand the difference between millilitres and volume.
Milliliters are a measurement of volume or space. A millilitre of water, a millilitre of gold, or a millilitre of air all occupy the same amount of space. The volume of an object changes as it is crushed to make it smaller and denser. One millilitre is equal to around twenty drops of water, or 1/5 of a teaspoon.
2. How do you calculate mass from volume?
Density equals mass divided by volume.
Rho=mass/volume
Yes, we can calculate mass based on volume. To accomplish so, we only need to be aware of the density of the specific substance under consideration.
Volume Calculated
Enter the object's volume and choose the appropriate volumetric units.
Substance Density is a measure of how dense a substance is.
Fill in the density of the material you're measuring.
Calculation of Mass
This is the object's computed mass, which you can convert to any mass measurement unit.
3. Let us know what you think about the difference between surface area and volume.
The total area of all the surfaces of a solid object is known as the surface area. The surface area is calculated in square units.
Volume is the sum of a 3-D solid's three sides (edges). It is measured in cubic units.
4. What is surface area?
The area is the amount of space occupied by a two-dimensional flat surface. It is based on square measuring units. The area filled by a three-dimensional object's outer surface is its surface area. In addition, it is measured in square units.
In general, there are two sorts of areas:
(I) total surface area
(ii) Lateral Surface Area/Curved Surface Area
Total surface area
The total surface area includes the base(s) as well as the curving component. It is the whole area covered by the object's surface. The total area of a shape with a curved surface and base is equal to the sum of the two areas.
Curved surface area
It is based on square measuring units. The area filled by a three-dimensional object's outer surface is its surface area. For shapes like a cylinder, it's also known as lateral surface area.
5. Is it possible to calculate the volume of a cylinder using the diameter of a sphere?
Yes, here's how to figure it out. The diameter of the sphere is d = 2r. As a result, the sphere's area is A = 2π r\[^{2}\] The cylinder, on the other hand, is a little different. If h (cylinder height) Equals r (sphere radius), we may compute the volume of the cylinder as V = 2πr\[^{2}\]h = 2πr\[^{3}\].
The volume of a sphere is used to determine its capacity. It's the area that the spherical takes up. Cubic units, such as m3, cm3, in3, and so on, are used to measure the volume of a sphere. The sphere is round and three-dimensional in shape. The x-axis, y-axis, and z-axis are the three axes that form their shape. All items with volume, such as football and basketball, are instances of spheres.
The density of a cylinder is its volume, which indicates the quantity of material it can carry or how much of any material can be immersed in it. The volume of a cylinder is calculated using the formula πr^2h, where r is the radius of the circular base and h is the cylinder's height. The material could be a liquid or any other substance that can be uniformly filled in the cylinder.
