How to find the Volume of a Triangular Pyramid?
A triangular pyramid is solid with a triangular base and triangles having a shared vertex on all three lateral faces. It’s a tetrahedron with equilateral triangles on each of its four faces. It has a triangle base and four triangular faces, three of which meet at one vertex. A right triangular pyramid’s base is a right-angled triangle, with isosceles triangles on the other faces. All of the faces of a regular triangular pyramid are equilateral triangles and it contains six symmetry planes.
Volume of a Triangular Pyramid
The amount of space occupied by a triangular pyramid in a 3D plane is called its volume. To put it another way, volume specifies the confined area or region of the pyramid. Knowing the base area and height of a triangular pyramid is enough to calculate its volume. Its formula equals one-third the product of base area and height. It is measured in units of cubic meters (m3).
V = 1/3 × B × h
Where,
V is the volume,
B is the base area,
h is the height of pyramid.
If we are given a regular triangular pyramid consisting of equilateral triangles, its volume is given by the formula,
V = a3/6√2
Where,
V is the volume,
a is the side length.
How to Find the Volume of a Triangular Pyramid?
Let’s take an example to understand how we can calculate the volume of a triangular pyramid.
Example: Calculate the volume of a triangular pyramid of base area 90 sq. m and height 6 m.
Step 1: Note the base area and height of a triangular pyramid. In this example, the base area of the pyramid is 90 sq. m and height is 6 m.
Step 2: We know that the volume of a triangular pyramid is equal to 1/3 × B × h. Substitute the given value of base area and height in the formula.
Step 3: So, the volume of triangular pyramid is calculated as, V = (1/3) × 90 × 6 = 180 cu. m
Sample Problems
Problem 1: Calculate the volume of a triangular pyramid with a base area of 50 sq. m and a height of 4 m.
Solution:
We have,
B = 50
h = 4
Using the formula we get,
V = 1/3 × B × h
= (1/3) × 50 × 4
= 66.67 cu. m
Problem 2: Calculate the volume of a triangular pyramid with a base area of 120 sq. m and a height of 10 m.
Solution:
We have,
B = 50
h = 4
Using the formula we get,
V = 1/3 × B × h
= (1/3) × 120 × 10
= 400 cu. m
Problem 3: Calculate the base area of a triangular pyramid if its volume is 300 cu. m and height is 15 m.
Solution:
V = 300
h = 15
Using the formula we get,
V = 1/3 × B × h
=> B = 3V/h
=> B = 3 (300)/15
=> B = 60 sq. m
Problem 4: Calculate the base area of a triangular pyramid if its volume is 600 cu. m and height are 5 m.
Solution:
V = 600
h = 5
Using the formula we get,
V = 1/3 × B × h
=> B = 3V/h
=> B = 3 (600)/5
=> B = 360 sq. m
Problem 5: Calculate the height of a triangular pyramid if its volume is 200 cu. m and the base area is 60 sq. m.
Solution:
We have,
V = 200
B = 60
Using the formula we get,
V = 1/3 × B × h
=> h = 3V/B
=> h = 3 (200)/60
=> h = 10 m
Problem 6: Calculate the height of a triangular pyramid if its volume is 150 cu. m and the base area is 50 sq. m.
Solution:
We have,
V = 150
B = 50
Using the formula we get,
V = 1/3 × B × h
=> h = 3V/B
=> h = 3 (150)/50
=> h = 9 m
Problem 7: Calculate the volume of a regular triangular pyramid if the side length is 10 m.
Solution:
We have,
a = 10
Using the formula we get,
V = a3/6√2
= (10)3/6√2
= 117.85 cu. m