Demonstration: Volume of a Pyramid and a Prism

In this video you will see how the volume of a pyramid is 1/3 the volume of a prism that has an equal shaped base and height.

For example, the formula for the volume of a triangular prism is 1/2 base area * height.

The formula for the volume of a triangular pyramid equals 1/3 ( 1/2 base area * height)

Therefore, the ratio of the volume of the pyramid is 3:1 compared to the volume of the prism.

In this demonstration I filled up three pyramids with water and poured them into an equally sized triangular prism.After pouring, the water was at the very top of the prism.

The demonstration shows you visually what the formulas show you Mathematically.

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Demonstration Volume of a Prism and a Square Pyramid

The volume of a pyramid is exactly 1/3 the volume of a prism that has an equal sized base and height.

This video demonstrates this fact by filling up three square pyramids with water, and pouring them into a prism.

You will see the volume of the three pyramids is exactly the volume of one prism.

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Volume of a pyramid

Video of the day
Volume of a pyramid
How do you find the volume of a pyramid. The formula equals 1/3 x base x height. There are two important points to remember when finding the volume of a pyramid.
First, the formula for finding the base will vary according to the shape of the base.
Here is a helpful link for a list of most base area formulas.
Second, the height is actually the altitude of the pyramid.

Use the formula 1/3base area times height in order to find the volume of a pyramid.
The video explains how you first find the base area and then the height of the pyramid and add these together and you have the volume

Video Guide
00:09 What is a pyramid?
00:33 Difference between a pyramid and a prism
00;42 Volume of Pyramid formula
01:06 Looking at pyramids with different bases and the different base area formulas
02:31 Sample problem-Finding volume of a pyramid with a square base
03:08 Sample problem- Finding volume of a pyramid with a right triangle base
For more on volume of a pyramid see
http://www.moomoomath.com/Volume-of-a-Pyramid.html
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Volume of a pyramid

Volume of a pyramid

Volume of a pyramid video

What is a pyramid? A pyramid is a three dimensional figure that has a base and an apex which you can think of as a point.

The formula for volume equals 1/3 * base * height

The base area will depend on the shape of the base.

For example if the shape of the base is a square you would just multiple length times width

If the shape is a triangle you would take ½ base * height to get the base and then multiply this by the height of the triangle.

Check here for a list of base area formulas.

Problem 1. Find the volume of a pyramid with a square base that has a side of 4 units and a height of 5 units.

 

Step 1. Find the base area 4 * 4 = 16 units

Step 2. Multiply base area times height = 16* 5 = 80 units

Step 3. Multiply this by 1/3 ( remember the formula is 1/3 * base * height = 1/3*80 = 26.6 units cubed

Problem 2. Find the volume of a pyramid with a triangle base with a base of 6 units and a height base of 8 units and a pyramid height of 7 units

 

 

 

 

Step 1. Find the base area using the formula ½ base * height

Step 2. ½ * 6 * 8 = 24 units

Step 3. Find the volume using 1/3 * base * height3

Step 4. 1/3 * 24 * 7 = 8*7

Step 5. 8*7 = 56 units cubed

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