Table of Contents
Last modified on August 3rd, 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 m3, cm3, mm3, ft3, or in3. 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.
As we know,
The edge length determines the size of a cube,
Volume (V) = a3, here a = 5 units
= 53
= 125 cubic units
What is the volume of a 9 inch cube?
As we know,
Volume (V) = a3, here a = 9 in
= 93
= 729 in3
Calculate the volume of a 40ft high cube container.
As we know,
The length, breadth, and height of a cube is same,
Volume (V) = a3, here a = 40 ft
∴ V = 403
= 64000 ft3
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 = a3, — (2)
Now, replacing the value of a in eqn (1)
a = d/√3, from (1)
V = a3 = (d/√3)3 replacing the value of a from (1)
= d3/(√3 × √3 × √3)
= √3d3/9
∴ V = ${\dfrac{\sqrt{3}}{9}d^{3}}$
(V = √3d3/9)
Calculate the volume of a cube given its diagonal 3 cm.
As we know,
Volume (V) = ${\dfrac{\sqrt{3}}{9}d^{3}}$, here d = 3 cm
∴ V = √3 × 33/9
= 5.2 cm3
finding the EDGE of a cube when the VOLUME is known
Calculate the side length of a cube given its volume 343 cubic millimeters.
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 mm3
${a=\sqrt[3] {343}}$
= 7 mm
Last modified on August 3rd, 2023