The volume of what polyhedron is determined by multiplying the product of the base area times the height?

The volume of what polyhedron is determined by multiplying the product of the base area times the height?

• A. Pyramid
• B. Cube
• C. Prism
• D. Cylinder

Answer: (C)

The volume of a prism is calculated by multiplying the area of the base by the height. This relationship holds true for all types of prisms, which can have different shapes for their bases, such as triangles, rectangles, or hexagons. The consistent formula for a prism stems from the fact that it is essentially made up of congruent cross-sections or bases stacked along a given height. In mathematical terms, if \( B \) represents the area of the base and \( h \) represents the height of the prism, the volume \( V \) can be expressed as: \[ V = B \times h \] Each of the other options has different volume formulas. For instance, the volume of a pyramid involves taking one-third of the base area multiplied by the height, and similarly, while the volume of a cylinder is based on the area of a circular base multiplied by the height, it does not encompass equating the volume to just the product of base area and height. The cube is a special case of a prism but has a specific formula due to its equal edge lengths. Therefore, the correct answer is associated with the general volume formula for prisms.

The volume of a prism is calculated by multiplying the area of the base by the height. This relationship holds true for all types of prisms, which can have different shapes for their bases, such as triangles, rectangles, or hexagons. The consistent formula for a prism stems from the fact that it is essentially made up of congruent cross-sections or bases stacked along a given height.

In mathematical terms, if ( B ) represents the area of the base and ( h ) represents the height of the prism, the volume ( V ) can be expressed as:

[ V = B \times h ]

Each of the other options has different volume formulas. For instance, the volume of a pyramid involves taking one-third of the base area multiplied by the height, and similarly, while the volume of a cylinder is based on the area of a circular base multiplied by the height, it does not encompass equating the volume to just the product of base area and height. The cube is a special case of a prism but has a specific formula due to its equal edge lengths. Therefore, the correct answer is associated with the general volume formula for prisms.