Question

A rectangular pyramid is placed on the top of a rectangular prism of height 7 ft and width one-third of its length. If both have the same base area and the total height of the structure is19 ft, which has a greater volume?

Answer 1

The prism and the pyramid share a common base so their length and width are the same.
Let l be the length of the prism and the pyramid.
Then, width $=\frac{l}{3}$
Height of the prism $=7$ ft
Volume of the prism = Base area $\times$ Height $=(l\times \frac{l}{3})\times 7=\frac{7}{3}{l}^2$