If a pyramid has an area of base 'B' and height 'h', what is the volume?

If a pyramid has an area of base 'B' and height 'h', what is the volume?

• A. 1/2 x B x h
• B. 1/3 x B x h
• C. B x h
• D. 2/3 x B x h

Answer: (B)

The volume of a pyramid can be calculated using the formula \( \text{Volume} = \frac{1}{3} \times B \times h \), where \( B \) represents the area of the base and \( h \) is the height of the pyramid. This formula reflects the fact that the volume of a pyramid is one-third of the product of the base area and the height because a pyramid can be visualized as a cone that tapers to a point at the top, and it occupies less space compared to a prism with the same base and height. The reasoning behind the one-third factor is based on the geometric relationship between pyramids and prisms. If you imagine filling a prism with the same base area and height, the prism will completely fill the space while the pyramid will only occupy a third of that space, demonstrating the volumetric difference. Other options do not conform to this geometric principle and therefore do not accurately represent the volume of a pyramid. For instance, multiplying the base area by the height without the one-third factor overestimates the volume, while the factor of one-half does not relate to the dimensions of a pyramid, and the two-thirds factor also inaccurately represents the relationship. Thus, the formula

The volume of a pyramid can be calculated using the formula ( \text{Volume} = \frac{1}{3} \times B \times h ), where ( B ) represents the area of the base and ( h ) is the height of the pyramid. This formula reflects the fact that the volume of a pyramid is one-third of the product of the base area and the height because a pyramid can be visualized as a cone that tapers to a point at the top, and it occupies less space compared to a prism with the same base and height.

The reasoning behind the one-third factor is based on the geometric relationship between pyramids and prisms. If you imagine filling a prism with the same base area and height, the prism will completely fill the space while the pyramid will only occupy a third of that space, demonstrating the volumetric difference.

Other options do not conform to this geometric principle and therefore do not accurately represent the volume of a pyramid. For instance, multiplying the base area by the height without the one-third factor overestimates the volume, while the factor of one-half does not relate to the dimensions of a pyramid, and the two-thirds factor also inaccurately represents the relationship. Thus, the formula