 |
VOOZH | about |
|
VOOZH | about |
Volume of a regular tetrahedron is a3/(6√2) where a is the edge of the tetrahedron. A pyramid with a triangular base is called a tetrahedron, it is a solid with four triangular faces.
In this article, we will explore how to find the volume of tetrahedrons with solved examples related to the volume of tetrahedrons.
Table of Content
A tetrahedron is a pyramid with a triangular base. It consists of 4 triangles forming a pyramid. In other words, a tetrahedron is a 3-D shape with 4 triangles and 6 edges. The below diagram represents a tetrahedron.
To find the volume of a tetrahedron we use the formula of volume of tetrahedron. In this formula we first find the cube of edge of tetrahedron and then divide it by 6√2. The resultant value gives us the volume of the tetrahedron.
Formula for the volume of tetrahedron is given by:
Volume of Tetrahedron = a3 / (6√2)
where,
In this formula we first find three vectors from given four points. Then we apply the formula:
Volume of Tetrahedron = (1/6) × Scalar Product of Three Vectors determined from Given 4 Points
Various Tetrahedron formulas are:
Area of One Face of Regular Tetrahedron Formula | A = 1/4√(3)a2 |
Total Surface Area of Regular Tetrahedron Formula | A = a2√(3) |
Slant Height of a Regular Tetrahedron Formula | l = a√(3/2) |
Altitude of a Regular Tetrahedron Formula | h = a√(6)/3 |
Volume of a Regular Tetrahedron Formula | V = a3√(2)/12 |
Read More:
Example 1: Find the volume of the tetrahedron with edge 6 units.
Solution:
Volume of tetrahedron is given by:
Volume of Tetrahedron = a3 / (6√2)
Volume of tetrahedron = 63 / (6√2)
= 36 / (√2)
= 18√2 cubic units.
Example 2: If edge of the tetrahedron is 4 units then, find the volume of tetrahedron.
Solution:
Volume of tetrahedron is given by:
Volume of Tetrahedron = a3/(6√2)
Volume of tetrahedron = 43 / (6√2)
= 64/ (6√2)
= 32 / (3√2)
= (16√2) / 3 = 7.54 cubic units
Example 3: Find the edge of the tetrahedron if the volume of tetrahedron given is 144√2 cubic units.
Solution:
Volume of tetrahedron is given by:
Volume of Tetrahedron = a3/(6√2)
a3 = Volume of tetrahedron × 6√2
a3 = 144√2 × 6√2
a3 = 1728
a = ∛1728
a = 12 units
Therefore, the edge of given tetrahedron is 12 units.
1. Find the volume of the tetrahedron with edge 18 units.
2. If edge of the tetrahedron is 9 units then, find the volume of tetrahedron.
3. Find the edge of the tetrahedron if the volume of tetrahedron given is 52 cubic units.
4. Determine the volume of a tetrahedron with an edge length of 10 units.
5. Calculate the volume of a tetrahedron given that its edge length is 15 units.
6. If the volume of a tetrahedron is 80 √2 cubic units, find its edge length.
7. Find the volume of a tetrahedron with an edge length of 3 units.
8. Given a tetrahedron with a volume of 27 cubic units, find the edge length.
9. Calculate the volume of a tetrahedron with an edge length of 12 units.
10. Find the edge length of a tetrahedron if its volume is 54√2 cubic units.
