What is Volume in Math? Measurement of Volume

What is Volume?

It is the amount of space taken up by three dimensional (3 D) body

Observe the below empty water tanker.

What is volume in Math

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

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} \ }

Formula for volume of cube

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

Example of cube

Hence, on multiplication we get area of square

(b) Adding third dimension by multiplying with width

Volume = Length x Height x Width

What is volume of cube

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

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

formula for volume of cuboid

Volume of Cylinder

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}

r = radius of the base circle
h = height of the cylinder

formula for volume of 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

Volume of cylinder formula explanation

(b) Adding new dimension by multiplication with height

cylinder example in Math

Hence the final formula becomes:

\mathsf{Volume\ =\ \pi \ \times r^{2} \times h}

Volume of Cone

What is 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}

r = radius of circular base
h = height of the cone

Formula for volume of cone

Volume of Sphere

Learn about sphere volume for students of USA, Canada, UK as per GCSE and Saxon Math

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}}

r = radius of sphere

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