6th grade Q4

The volume of a pyramid is exactly one third the volume of a prism with the same base area and height.

Here's a breakdown of how that works:

1. Volume of a prism:

where $B$ is the area of the base of the prism, and $h$ is the height.

1. Volume of a pyramid:

where $B$ is the area of the base of the pyramid, and $h$ is the height.

Comparing these two formulas shows that the volume of the pyramid is one third that of the prism when both shapes have identical bases and heights.

Example:

If a prism has the volume of 30 cubic units, the pyramid with the same base and height has the volume of 10 cubic units.

This relationship can be visualized by imagining filling a cone with water and pouring it into a cylinder of the same dimensions; it would take exactly three cones of water to fill the cylinder completely.