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 Triangular Pyramid and Triangular Prism

Watch this demonstration in order to understand why the volume of a triangular pyramid is 1/3 the volume of a triangular prism.



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



In order to demonstrate this fact I used a triangular shaped plastic prism and pyramid and filled them with water. What you will see is that when you fill the pyramid up with water, and pour this amount into the prism , that it takes exactly three pyramids to fill one prism.



Hopefully this visual demonstration will help you understand how the formulas for finding the volume of a prism and pyramid are derived.

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Surface Area Formula Chart

The chart includes formulas for surface area,volume, and lateral area for a cone,cylinder, cube, prism,pyramid, and a sphere.


For more information please see: MooMooMath/Surface Area Formula Chart

Feel free to embed

<iframe width="600" height="1015" frameborder="0" scrolling="no" style="overflow-y:hidden;" src="https://magic.piktochart.com/embed/2288542-surface-area"></iframe>

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Rectangular Prisms

I need help with rectangular prisms !!





I have also produced several videos that will help you with rectangular prisms

This video gives step by step directions for finding the surface area of a rectangular prism.

Video covers the basic properties of a rectangular prism

Videos gives step by step directions for finding the surface area of a prism. Includes finding the area of a hexagonal prism.

For even more information on prisms please see Rectangular Prisms

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How to find the surface area of a prism

How to find the surface area of a prism

Surface Area of a Prism

First, what is a prism? A prism is a rectangular solid with a length, a width, and a height.

To find the surface area you are trying to figure out the total area of the surface of the prism.

The formula for finding the surface area equals

2* (length *width) + 2(length*height) + 2*(height * width) = Surface area of a prism

Find the surface area of a prism with a length of 6 units, a height of3 units and a width of 4 units.

Step 1. Plug in the appropriate units in the formula

              2* (6*4) + 2(6*3) + 2( 3*4)

                   (L*W)      ( L*H)      (H*W)

Step 2. 2*24 + 2*18 + 2*12

Step 3. 48+36+24 = 108 units squared 

Surface area is always squared

 

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How to find the volume of a prism

Volume of a Prism

Here is the problem worked on video

What is a prism? A prism is a three dimensional figure with parallel bases.

The formula for finding the volume of a prism is just length X width X height

Let’s look at a problem

What is the volume of a prism with a base of 6 by 7 units and a height of 9 units?

 

Step 1 Plug the units into the formula l * w * h    6*7*9

Step 2. Multiply 6*7*9 = 42*9

            42*9 = 378 units cubed (volume is always cubed)

 

Now a prism can be have different shaped bases. The key to finding the volume is to find the base area formula for that shape and then multiply this by the height.

Check here for a list of most base area formulas

For example, if you had a triangle shaped prism you would use ½ base x length x height to find the volume of the triangular prism

 

 

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