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Pyramid volume example Problem 3. 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 * height
Step 4. 1/3 * 24 * 7 = 8*7
Step 5. 8*7 = 56 units cubed
Use the formula for volume
l x w x h /3
Step 1 .Multiple the length * width* height
6 x 6 x 4 = 144
Step 2 Divide the l*w*h by 3
144/3= 48 units cubed
Volume of Pyramid = 48 units^3
Volume of a Pyramid
The formula for finding the Volume of a Pyramid is:
Volume is the amount of space found inside an object. We use volume all the time in everyday life. When you cook you use a measuring cup in order to have the correct volume of ingredients in the recipe, at the grocery store bottles are labeled by the volume of liquid they hold. In geometry you are often asked to find the volume of spheres, cubes, prisms, and other 3D objects. Each 3D object has a formula for finding volume based on it’s shape.
For a list of Base Area Formulas check here
Pyramid 1
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Volume pyramid example Problem 2. 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
Use length * width because of the square base
The height (altitude) of a pyramid is a perpendicular line drawn from the apex to the base of the pyramid. The apex of a pyramid is the vertex opposite the base and is the highest point of the pyramid. A common mistake made when calculating pyramid volume is to use the slant height instead of the height. (altitude)
What is the volume of pyramid 1 that has a base length of 6 units and a height of 4 units ?
The base area formula you use will vary according to the shape of the pyramid.
For instance, to find the volume of a rectangular pyramid use length times width for the base area.
To find the volume of a triangular pyramid use the base area formula ½ base times height.
Apex
Base Area
Volume of a Truncated Pyramid ( Frustum )
A Truncated pyramid (also called a frustum) look like a pyramid with the top removed.
One way to find the volume is to find the volume of the entire pyramid, and subtract the portion that has been removed.
The formula would look like this,
Volume of large pyramid-volume small pyramid
1/3Base x height-1/3Base x height
You can find the slant height of the entire pyramid using a proportion, and then the Pythagorean theorem to find the altitude of both pyramids.
I have created a video with step by step directions for finding the volume of a truncated pyramid.