Unit 7 lesson 4 relationship between volume of prisms and pyramids

Answer 1

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.