Which of the following shapes does NOT use the formula V = 1/3Bh for calculating volume?

Which of the following shapes does NOT use the formula V = 1/3Bh for calculating volume?

• A. Triangular prism
• B. Triangular pyramid
• C. Cone
• D. All of the above

Answer: (A)

The volume formula V = 1/3Bh is specifically associated with three-dimensional shapes that have a triangular base and taper to a point. This formula indicates that you take one-third of the area of the base (B) multiplied by the height (h) of the shape. The triangular pyramid uses this formula because it has a triangular base and meets at a vertex, allowing for the height to be measured directly from the base to the apex. Similarly, a cone also applies this formula as it features a circular base and tapers to a point, with the general volume formula being analogous to the frustum of a cone. In the case of a triangular prism, the calculation for volume uses the formula V = Bh, where B is the area of the base (which is triangular in this case) and h is the height of the prism. Since this shape does not taper to a point, the one-third factor in the formula is not applicable, making it distinguishable from the other shapes that do utilize it. Thus, the triangular prism does not use the formula V = 1/3Bh for volume, making it the exception among the options provided.

The volume formula V = 1/3Bh is specifically associated with three-dimensional shapes that have a triangular base and taper to a point. This formula indicates that you take one-third of the area of the base (B) multiplied by the height (h) of the shape.

The triangular pyramid uses this formula because it has a triangular base and meets at a vertex, allowing for the height to be measured directly from the base to the apex. Similarly, a cone also applies this formula as it features a circular base and tapers to a point, with the general volume formula being analogous to the frustum of a cone.

In the case of a triangular prism, the calculation for volume uses the formula V = Bh, where B is the area of the base (which is triangular in this case) and h is the height of the prism. Since this shape does not taper to a point, the one-third factor in the formula is not applicable, making it distinguishable from the other shapes that do utilize it.

Thus, the triangular prism does not use the formula V = 1/3Bh for volume, making it the exception among the options provided.