Question

A landscape architect uses molds for castingrectangular pyramids and rectangular prisms to makegarden statues. He plans to place each finishedpyramid on top of a prism. If one batch of concretemix makes one prism or three pyramids, how doesthe volume of one pyramid compare to the volume ofone prism? Explain.

Answer 1

Volume of a rectangular pyramid:

`V=(1)/(3)(L\cdot W)\cdot h`

Volume of a rectangular prism:

`V=L\cdot W\cdot h`

As you can see the volume of a rectangular pyramid (y) is a thrid part of the volume of a rectangular prism (x). Then, if the length, width and height of both molds is the same the volume of the rectangular prism (x) is three times the volume of the volume of the rectangular pyramid (y).

`\begin{gathered} x=3y \\ y=(1)/(3)x \end{gathered}`