Question

determining when the volumes of pyramids are the same
if two pyramids have the same height, what must be true of the pyramids for them to also have the same volume?
○ the pyramids must have the same base shape.
○ the pyramids must have the same slant height.
○ the areas of the bases must be the same.
○ the pyramids must be identical in size and shape.

Explanation:

The volume of a pyramid is given by the formula $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. If two pyramids have the same height ($h_1=h_2$), setting their volumes equal ($V_1=V_2$) gives $\frac{1}{3}B_1h_1=\frac{1}{3}B_2h_2$. Since $h_1=h_2$, the $\frac{1}{3}$ and height terms cancel out, leaving $B_1=B_2$. Base shape, slant height, or identical size/shape are not required, only equal base areas.

Answer:

The areas of the bases must be the same.