Which generalization of the volume of pyramids or cones is true?(1 point)

Responses

The volume of a pyramid or cone is one-half the volume of the larger shape that it comes from.
The volume of a pyramid or cone is one-half the volume of the larger shape that it comes from.

The volume of a pyramid or cone is equal to the volume of the larger shape that it comes from.
The volume of a pyramid or cone is equal to the volume of the larger shape that it comes from.

The volume of a pyramid or cone is one-fourth the volume of the larger shape that it comes from.
The volume of a pyramid or cone is one-fourth the volume of the larger shape that it comes from.

The volume of a pyramid or cone is one-third the volume of the larger shape that it comes from.

1 answer

The correct generalization of the volume of pyramids or cones is:

The volume of a pyramid or cone is one-third the volume of the larger shape that it comes from.

In mathematical terms, if the base area of the pyramid or cone is \( B \) and its height is \( h \), the volume \( V \) is given by the formula:

\[ V = \frac{1}{3} B h \]