# Volume of Cube || Finding Volume of Cube

## What is cube?

Cube is a 3D shape of a square.

The Cube has 6 square faces, 8 vertices and 12 edges.

Like square, all the sides of cube are equal in length and all the vertices angle measures 90 degree

Features of Cube
(a) 3D shape of square
(b) 6 Square faces
(c) All sides are equal in length

Example of Cube

Rubik’s cube is one of the most common example of cube found in dailylife.

## What is Volume of Cube?

Volume of cube is the amount of space captured inside the cube.

Consider the cubic aquarium above.

The volume of water used to fill the aquarium to brink is equal to the volume of the cube.

Hence, the total space captured by the cube is called volume of cube.

In the above figure, the empty space is filled with air, but you can use it to fill it with water.

## Volume of Cube Formula

The formula for volume of cube is:

Volume = Length x Breadth x Height

We know that in cube, side lengths are same

Let side = a

\mathtt{V\ =\ a^{3}}

## Cube Volume – Formula Explanation

The formula for volume of cube is;

Volume of cube = Side x Side x Side

Let us understand the formula step by step:

Step 01
When we multiply Side x Side, we get area of one face of square

Step 02
When we include third side in the formula, we introduce new dimension in the cube

You can see that third dimension is included backwards to make the figure three dimensional.

That’s how we get formula;
Volume = Side x Side x Side

## Unit of Volume

The volume of cube (or any object) is measured in cubic units

Explanation

Given above is the cube of side a meter

Volume of cube
= Length x Breadth X Height

= a meter x a meter x a meter

= \mathtt{Volume\ =a^{3} \ m^{3} \ }

See that the volume is expressed in \mathtt{m^{3} \ } {cubic units}

Infact, whenever you see any data with units like \mathtt{\ m^{3} ,\ cm^{3} \ } etc. , make a note that data is about the volume

## Finding length of cube using volume data

How to find side length of cube when volume data is given?

The method is very simple.

Let the volume of cube given is V

We know that:
Volume of Cube = Length x Breadth x Height

We also know that;
In cube, the length of all sides are equal
Let the side length be a

Now the formula becomes

\mathtt{V=\ a\ \times a\ \times \ a}\\\ \\ \mathtt{V\ =\ a^{3}}\\\ \\ \mathtt{a\ =\ \sqrt[3]{V}}

Example
The volume of cube is 512 \mathtt{( cm)^{3}}\ . Find the side length of the cube.

Given:
Volume of cube (V) = 512 \mathtt{( cm)^{3}}\\\ \\

\mathtt{We\ have\ seen\ that}\\\ \\ \mathtt{Side\ =\ \sqrt[3]{V}}\\\ \\ \mathtt{Putting\ the\ value\ of\ V}\\\ \\ \mathtt{Side\ =\sqrt[3]{512\ cm^{3}}}\\\ \\ \mathtt{Side\ =\ 8\ cm}

## Finding Volume of cube when total surface area is given

What is total surface area of cube?

We know that cube is made by joining six squares of equal sides

Area of 1 Face = \mathtt{a\ \times a\ =\ a^{2}}

Total Surface Area of Cube = Area of 6 Face

S = \mathtt{6\ a^{2}}\

When total surface area of cube is given, you can find volume of cube using following steps:

Step 01
Find the side length using total surface Area

Let S be total surface area

\mathtt{S\ =\ 6\ a^{2}}\\\ \\ \mathtt{a\ =\ \sqrt{\frac{S}{6}}}

Step 02
Now find volume of cube using formula

\mathtt{Volume\ =\ ( a)^{3}}

## Volume of cube questions

(01) Find the volume of cube of side 3 meter

Given
Side of cube (a) = 3 meter

\mathtt{we\ know\ that}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 3)^{3} \ =\ 27\ m^{3}}

Hence, 27 \mathtt{m^{3}} is the solution

(02) The total surface area of cube is 24 sq. cm. Find the volume of cube

Given
Surface area of cube = 24 sq cm

\mathtt{We\ know\ that}\\\ \\ \mathtt{Surface\ area\ of\ cube\ =\ 6\ a^{2}}\\\ \\ \mathtt{24\ =\ 6\ a^{2}}\\\ \\ \mathtt{a^{2} \ =\ 4}\\\ \\ \mathtt{a\ =\ 2\ cm}

Hence side length of cube is 2 cm

Now let us find the volume of cube;

\mathtt{we\ know\ that}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 2)^{3} \ =\ 16\ cm^{3}}

(03) Find the volume of below cube

Given
Side length (a) = 10 meter

We know that in cube all sides are equal

Formula for Volume of cube is;
\mathtt{Volume\ of\ cube\ =\ ( a)^{3}}\\\ \\ \mathtt{Volume\ of\ cube\ =\ ( 10)^{3} \ =\ 1000\ m^{3}}