Table of Contents

Last modified on March 28th, 2023

The volume of a cube is the space it takes up in the three-dimensional plane. It is measured in cubic units such as m^{3}, cm^{3}, mm^{3}, ft^{3}, or in^{3}. The volume of a cube determines how big it is.

The basic or common formula to determine the volume of a cube is:

Let us solve some examples involving the above formula.

**Find volume of a 5 x 5 cube.**

Solution:

As we know,

The edge length determines the size of a cube,**Volume ( V) = a^{3}**, here a = 5 units

= 5

= 125 cubic units

**What is the volume of a 9 inch cube?**

Solution:

As we know,**Volume ( V) = a^{3}**, here a = 9 in

= 9

= 729 in

**Calculate the volume of a 40ft high cube container.**

Solution:

As we know,

The length, breadth, and height of a cube is same,**Volume ( V) = a^{3}**, here a = 40 ft

∴ V = 40

= 64000 ft

The formula to get the volume of a cube when the diagonal is known is:

**Derivation**

Here we will use the equation of the diagonal to derive the formula of volume of a cube with diagonal.

Length of Space Diagonal (d) = ${\sqrt{3}a}$ — (1)

The equation for volume of a cube with edge length is V = a^{3}, — (2)

Now, replacing the value of a in eqn (1)

a = d/√3, from (1)

V = a^{3} = (d/√3)^{3} replacing the value of a from (1)

= d^{3}/(√3 × √3 × √3)

= √3d^{3}/9

∴ V = ${\dfrac{\sqrt{3}}{9}d^{3}}$

(V = √3d^{3}/9)

**Calculate the volume of a cube given its diagonal 3 cm.**

Solution:

As we know,**Volume ( V) = **${\dfrac{\sqrt{3}}{9}d^{3}}$, here d = 3 cm

∴ V = √3 × 3

= 5.2 cm

finding the **EDGE** of a cube when the **VOLUME** is known

**Calculate the side length of a cube given its volume 343 cubic millimeters.**

Solution:

Side length of a cube is actually its edge length. Oftentimes the edge is termed as side length.

So, we will use an alternative formula to find the edge with the volume,

${a=\sqrt[3] {V}}$, here V = 343 mm^{3}

${a=\sqrt[3] {343}}$

= 7 mm

Last modified on March 28th, 2023