Unit 7 lesson 4 relationship between volume of prisms and pyramids
The relationship between the volume of prisms and pyramids is that they both involve finding the product of the base area and the height of the shape.
For a prism, the volume is calculated by multiplying the area of the base by the height of the prism. The formula is V = Bh, where V is the volume, B is the area of the base, and h is the height.
For a pyramid, the volume is calculated by multiplying the area of the base by the height of the pyramid and dividing by 3. The formula is V = (1/3)Bh, where V is the volume, B is the area of the base, and h is the height.
Since both formulas involve the product of the base area and height, the volume of pyramids is always one-third of the volume of a corresponding prism with the same base and height. This relationship can be demonstrated by dividing the volume of a prism by 3 to find the volume of a pyramid with the same base and height.
In summary, the relationship between the volume of prisms and pyramids is that the volume of a pyramid is always one-third of the volume of a prism with the same base and height.