High School Math : How to find the volume of a pyramid
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Example Questions
Example Question #1 : Pyramids
What is the volume of a pyramid with a height of 
To find the volume of a pyramid we must use the equation
We must first solve for the area of the square using
We plug in 
We then plug our answer into the equation for the pyramid with the height to get
We multiply the result to get our final answer for the volume of the pyramid
Example Question #1 : Pyramids
Find the volume of the following pyramid. Round the answer to the nearest integer.
The formula for the volume of a pyramid is:
where 
In order to determine the height of the pyramid, you will need to use the Pythagoream Theorem to find the slant height:
Now we can use the slant height to find the pyramid height, once again using the Pythagoream Theorem:
Plugging in our values, we get:
Example Question #2 : Pyramids
Find the volume of the following pyramid.
The formula for the volume of a pyramid is:
Where 
Use the Pythagorean Theorem to find the length of the slant height:
Now, use the Pythagorean Theorem again to find the length of the height:
Plugging in our values, we get:
Example Question #1 : Pyramids
What is the sum of the number of vertices, edges, and faces of a square pyramid?
A square pyramid has one square base and four triangular sides.
Vertices (where two or more edges come together): 5. There are four vertices on the base (one at each corner of the square) and a fifth at the top of the pyramid.
Edges (where two faces come together): 8. There are four edges on the base (one along each side) and four more along the sides of the triangular faces extending from the corners of the base to the top vertex.
Faces (planar surfaces): 5. The base is one face, and there are four triangular faces that form the top of the pyramid.
Total
Example Question #1 : How To Find The Volume Of A Pyramid
An architect wants to make a square pyramid and fill it with 12,000 cubic feet of sand. If the base of the pyramid is 30 feet on each side, how tall does he need to make it?
Volume of Pyramid = 1/3 * Area of Base * Height
12,000 ft3 = 1/3 * 30ft * 30ft * H
12,000 = 300 * H
H = 12,000 / 300 = 40
H = 40 ft
Example Question #3 : Pyramids
The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?
Volume of a pyramid is
Thus:
Area of the base is 
Therefore, each side is 
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