Volume of Prisms & Pyramids Discussion
The volume of a prism is calculated by multiplying the base area of the prism by its height. The formula for the volume of a prism is V = Bh, where V is the volume, B is the base area, and h is the height.
For example, if you have a rectangular prism with a base area of 6 square units and a height of 4 units, the volume would be V = 6 * 4 = 24 cubic units.
On the other hand, the volume of a pyramid is calculated by multiplying the base area of the pyramid by its height and then dividing by 3. The formula for the volume of a pyramid is V = Bh/3, where V is the volume, B is the base area, and h is the height.
For example, if you have a square pyramid with a base area of 9 square units and a height of 3 units, the volume would be V = 9 * 3 / 3 = 9 cubic units.
In general, prisms have two parallel and congruent bases, while pyramids have one base and triangular sides that converge at a single point called the apex. Both shapes have volume formulas that involve the base area and height, but the division by 3 in the pyramid formula accounts for the fact that the sides slope inward towards the apex.