Relationships Between Volume of Prisms & Pyramids

Answer 1

The volume of a prism and a pyramid are both related to the base area and height of the shape.

For a prism, the volume can be calculated using the formula V = B * h, where B is the base area of the prism and h is the height of the prism. The base area is the area of the shape when viewed from the top, and the height is the perpendicular distance between the two base faces.

For a pyramid, the volume can be calculated using the formula V = (1/3) * B * h, where B is the base area of the pyramid and h is the height of the pyramid. The base area is the same as for the prism, and the height is the perpendicular distance from the base to the apex of the pyramid.

In both cases, the volume of the shape is directly proportional to the base area and height. This means that if you double the base area or height, the volume will also double.

Additionally, for both shapes, if the base area and height are the same, the volume will be the same. This is because the volume formula for both shapes is dependent on these two parameters.

Overall, the volume of prisms and pyramids is closely related to the base area and height of the shapes, and changes in these parameters will directly affect the volume of the shape.