# The Volume of Prisms and Pyramids

1. A triangular pyramid with a base length of 9 inches, a base height of 10 inches, and a height of 32 inches. Find the volume of the figure described.

2. A square pyramid with a base length of 4 cm and a height of 6 cm resting on top of a 4 cm cube. Find the volume of the figure described.

3. The square pyramid at the entrance of the Louvre Museum in Paris, FR is 35.42 meters wide and 21.54 meters tall. Find the volume of the Louvre Pyramid.

4. For prisms and pyramids, how are the area of the base of the solid and the shape of the solid related to the volume?

5a. A triangular prism and a triangular pyramid have congruent bases and heights. What is the relationship between the volumes of the two figures? Explain in words using an example.

b. Explain the relationship between the volumes using their formula.

https://brainmass.com/math/geometric-shapes/volume-prisms-pyramids-600621

#### Solution Preview

1. Volume=base area*height/3=9*10*32/3=960

2. Volume=base area*height/3=4*4*3/3=21.33

3. Volume=base area*height/3=35.42*35.42*21.54/3=9007.86

4. For prisms, the volume=base area*height

and for pyramids, the volume=base area*height/3

So the ...

#### Solution Summary

The solution gives detailed steps on calculating and discussing the volume of prisms and pyramids.