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# Volume of Cubes – Explanation & Examples

**The volume of a cube is defined as the number of cubic units occupied by the cube.**

A** cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices **in geometry. Each face of a cube is a square. In 3 – dimension, the cube’s sides are; the length, width, and height.

In the above illustration, **sides of a cube are all equal i.e. Length = Width = Height = a**

Cubes are everywhere! Common examples of cubes in the real world include square ice cubes, dice, sugar cubes, casserole, solid square tables, milk crates, etc.

The **volume of a solid cube is the amount of space occupied by the solid cube**. The volume is the difference in space occupied by the cube and the amount of space inside the cube for a hollow cube.

## How to Find the Volume of a Cube?

*To find the volume of a cube, here are the steps:*

- Identify the length of the side or length of the edge.
- Multiply the length by itself three times.
- Write the result accompanied by the units of volume.

Volume is measured in cubic units, i.e., cubic meters (m^{3}), cubic centimeters (cm^{3}), etc. We can also measure the volume in liters or milliliters. In such cases, the volume is known as capacity.

** **

## Volume of a Cube Formula

The volume of cube formula is given by;

**Volume of cube =length * width * height**

**V = a * a * a **

**= a ^{3} cubic units**

Where V= volume

a = The length of the edges.

Let’s try the formula with a few example problems.

*Example 1*

What is the volume of a cube whose sides are 10 cm each?

__Solution__

Given, the side length = 10 cm.

By the volume of a cube formula,

V = a^{3}

Substitute a = 10 in the formula.

V = 10^{3}

= (10 x 10 x 10) cm^{3}

= 1000 cm^{3}

Therefore, the volume of the cube is 1000 cm^{3}.

*Example 2*

The volume of a cube is 729 m^{3}. Find the side lengths of the cube.

__Solution__

Given, volume, V = 729 m^{3}.

a = ?

To get the side lengths of the cube, we find the cube root of the volume.

V = a^{3}

729 = a^{3}

^{3}√ 729 = ^{3}√ a^{3}

a = 9

So, the length of cube is 9 m.

*Example 3*

The edge of a Rubik’s cube is 0.06 m. Find the volume of the Rubik’s cube?

__Solution__

Volume = a^{3}

= (0.06 x 0.06 x 0.06) m^{3}

= 0.000216 m^{3 }

= 2.16 x 10 ^{– 4} m^{3}

*Example 4*

A cubical box of external dimensions 100 mm by 100 mm by 100 mm is open at the top. Suppose the wooden box is made of 4 mm wood thick. Find the volume of the cube.

__Solution__

In this case, subtract the thickness of the wooden box to get the dimensions of the cube.

Given, the cube is open at the top, so we have

Length = 100 – 4 x 2

= 100 – 8

= 92 mm.

Width = 100 – (4 x 2)

= 92 mm

Height = (100 – 4) mm…………. (a cube is open at the top)

= 96 mm

Now calculate the volume.

V= (92 x 92 x 96) mm^{3}

= 812544 mm^{3}

= 8.12544 x 10^{5} mm^{3}

*Example 5*

Cubical bricks of length 5 cm are stacked such that the height, width, and length of the stack is 20 cm each. Find the number of bricks in the stack.

__Solution__

To get the number of bricks in the stack, divide the stack’s volume by the brick volume.

Volume of the stack = 20 x 20 x 20

= 8000 cm^{3}

Volume of the brick = 5 x 5 x 5

= 125 cm^{3}

Number of bricks = 8000 cm^{3}/125 cm^{3}

= 64 bricks.

*Example 6*

How many cubical boxes of dimensions 3 cm x 3 cm x 3 cm can be packed in a large cubical case of length 15 cm.

__Solution__

To find the number of boxes that can be packed in the case, divide the case’s volume by the volume of the box.

Volume of each box = (3 x 3 x 3) cm^{3}

= 27 cm^{3}

Volume of the cubical case = (15 x 15 x 15) cm^{3}

= 3375 cm^{3}

Number of boxes = 3375 cm^{3}/27 cm^{3}.

= 125 boxes.

*Example 7*

Find the volume of a metallic cube whose length is 50 mm.

__Solution__

Volume of a cube = a^{3}

= (50 x 50 x 50) mm^{3}

= 125,000 mm^{3}

= 1.25 x 10^{5} mm^{3}

*Example 8*

The volume of a cubical solid disk 0.5 in^{3}. Find the dimensions of the disk?

__Solution__

Volume of a cube = a^{3}

0.5 = a^{3}

a = ^{3}√0.5

a = 0.794 in.

*Practice Questions*

- What is the volume of the 12 cm high cuboid whose length is 2 times its height and 4 times its width?
- A solid cube of equal lengths of 10 mm is cut into 8 cubic pieces of equal size. Find the length (in
*mm*) of the sides of the new cube.

__Answers__

- 1728 cubic cm
- 5 mm

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