What is Volume?
It is the amount of space taken up by three dimensional (3 D) body
Observe the below empty water tanker.
Currently the empty space is filled with air.
Now start pouring water into the container to the brim.
The amount of water stored in the tanker is the equal to the volume/ capacity of the tanker.
Earlier the space was filled with air and now it is filled with water.
Units of Volume
Volume is measured in cubic units
Remember how you calculated the area of square?
You multiplied Length x Breadth
If both length & breadth is given in meter, the the final unit of area will be:
\mathtt{Area\ of\ Square\ }\\\ \\ \mathtt{=\ meter\ \times \ meter\ }\\\ \\ \mathtt{=\ ( meter)^{2}}
Hence, the area is measured in square units
Now the formula for volume calculation is:
Volume = Length x Breadth x Height
If all the lengths is in meter, then;
\mathtt{Volume\ of\ cube\ }\\\ \\ \mathtt{=\ meter\ \times \ meter\ \times \ meter\ \ }\\\ \\ \mathtt{=\ ( meter)^{3}}
Hence, volume is measured in cubic units
How to measure Volume
In Mathematics, there are some formulas which will help you find the volume of some basic shapes.
Here we will discuss formulas for shape like:
(a) Cube
(b) Cuboid
(c) Cylinder
(d) Cone
(e) Sphere
Volume of Cube
Given above is the image of cube.
In a cube, all sides are of equal length.
Hence, measurement of length, breadth and width is same in above figure.
Volume of Cube is given by formula:
Volume = Length x Width x Height
In the above figure;
Length = Breadth = Height = a cm
\mathsf{Volume\ =\ a\ \times a\ \times \ a}\\\ \\ \mathsf{Volume\ =\ a^{3} \ }
Volume of Cube – Formula Explanation
We learnt that;
Volume of Cube = Length x Height x Width
Let us understand the formula step by step
(a) Multiply Length x Height
When we multiply Length x Height we are basically finding area
Hence, on multiplication we get area of square
(b) Adding third dimension by multiplying with width
Volume = Length x Height x Width
On including width in the formula, we have opened up the third dimension and on multiplication we get the volume of cube
Volume of Cuboid
Given above is the image of cuboid
A cuboid, the sides length, width and height have different length.
All the angles in cuboid measures 90 degree
Volume of cuboid is given by following formula:
Volume = Length x Breadth x Height
In the above figure;
Length = a cm
Height = b cm
Width = c cm
Putting the values in the formula
Volume = a x b x c cu. cm
Volume of Cylinder
Given above is the shape of cylinder with radius r and height h
Cylinder is made of two circular bases at the top & bottom attached with the curved surface in between
Volume of cylinder is given by formula:
\mathsf{Volume\ =\ \pi \ \times r^{2} \times h}
Where;
r = radius of the base circle
h = height of the cylinder
Volume of Cylinder – Formula Explanation
We know;
\mathsf{Volume\ =\ \pi \ \times r^{2} \times h}
Let us understand the component of the formula
(a) \mathsf{\pi \ \times r^{2}}
\mathsf{\pi \ \times r^{2}} finds the area of top circle
(b) Adding new dimension by multiplication with height
Hence the final formula becomes:
\mathsf{Volume\ =\ \pi \ \times r^{2} \times h}
Volume of Cone
Given above is the shape of cone with radius r and height h
The cone is made by base circle of radius r which narrows down to a point called Apex
Volume of Cone is given by formula
\mathtt{Volume\ =\ \frac{1}{3} \ \times \ \pi \ \times r^{2} \times h}
Where;
r = radius of circular base
h = height of the cone
Volume of Sphere
Given above is the shape of sphere with radius r
Sphere is one of the common shapes found in practical life.
If you like playing sport like Football, Cricket, Tennis etc., the shape of the ball is in form of sphere
Volume of sphere is given by formula
\mathtt{Volume\ =\ \frac{4}{3} \ \times \ \pi \ \times r^{3}}
Where;
r = radius of sphere
