Solved Examples of Diagonal of a Cube Formula
Example 1. Calculate the face diagonal of a cube of side length 2 m.
Solution:
We have,
a = 2
Using the formula we get,
d = √2.a
⇒ d = √2 (2)
⇒ d = (1.414) (2)
⇒ d = 2.83 m
Example 2. Calculate the face diagonal of a cube of side length 5 m.
Solution:
We have,
a = 5
Using the formula we get,
d = √2.a
⇒ d = √2 (5)
⇒ d = (1.414) (5)
⇒ d = 7.07 m
Example 3. Calculate the body diagonal of a cube of side length 3 m.
Solution:
We have,
a = 3
Using the formula we get,
D = √3.a
⇒ D = √3 (3)
⇒ D = (1.732) (3)
⇒ D = 5.196 m
Example 4. Calculate the body diagonal of a cube of side length 7 m.
Solution:
We have,
a = 7
Using the formula we get,
D = √3.a
⇒ D = √3(7)
⇒ D = (1.732) (7)
⇒ D = 12.12 m
Example 5. Calculate the side length if the face diagonal of a cube is 6 m.
Solution:
We have,
d = 6
Using the formula we get,
d = √2.a
⇒ a = d/√2
⇒ a = 6/√2
⇒ a = 4.24 m
Example 6. Calculate the side length if the body diagonal of a cube is 13√3 m.
Solution:
We have,
D = 13√3
Using the formula we get,
D = √3.a
⇒ a = D/√3
⇒ a = 13√3/√3
⇒ a = 13 m
Example 7. Calculate the body diagonal of a cube if its face diagonal is 9√2 m.
Solution:
We have,
d = 9√2
Find the side length.
d = √2.a
⇒ a = d/√2
⇒ a = 9√2/√2
⇒ a = 9 m
Now using the formula we get,
D = √3.a
⇒ D = √3 (9)
⇒ D = 15.58 m
Diagonal of a Cube Formula
Diagonal of a cube is the line segment joining the two non-adjacent vertices of a Cube. The diagonal of a cube formula helps us to calculate the length of diagonals in a cube. There are primarily two diagonals in a cube, namely face diagonals and body diagonals. In this article, we will learn the types of diagonals in a cube, the diagonal of a cube formula, the derivation of the diagonal of a cube formula, and problems based on it.