SOLUTION: How is the formula for volume of a prism like the formula for volume of a pyramid? How are they different? Help Please Thanks

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Question 139193: How is the formula for volume of a prism like the formula for volume of a pyramid? How are they different? Help Please Thanks
Answer by solver91311(24713) (Show Source):
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The formula for the volume of a prism is where is the area of the base and is the height.

The formula for the volume of a pyramid is where is the area of the base and is the height.

So a pyramid with a base equal in area to a prism and a height equal to the height of the prism has the volume. Notice that the bases don't necessisarily have to have the same shape -- just the same area. For example, if you had a prism with a triangular base where the base of the triangle was 2 and the altitude of the triangle was 1 and further the height of the prism was 5, then a square based pyramid with sides on the base of 1 unit and a height of 5 would have exactly the volume of the prism.

By the way, this same relationship holds between a cylinder and a cone. Equal base areas and equal heights implies a 3 to 1 ratio in the volumes. That makes perfectly good sense if you consider that a cone is just a pyramid with an infinite number of infinitessimally thin faces, and a cylinder is a prism with an infinite number of infinitessimally thin faces.

My 5th grade teacher (more years ago than I care to reveal) demonstrated this relationship. She had a set of clear plastic geometric solids. She filled the pyramid with sand three times and it filled the equal-based, equal-height prism exactly.