Answer:
equal
Step-by-step explanation:
Let's compare the volumes of the rectangular prism and the rectangular pyramid.
For the rectangular prism:
[tex] \textsf{Volume}_{\textsf{prism}} = l \times b \times h \\\\ = a \times b \times 2c\\\\ = 2abc[/tex]
For the rectangular pyramid:
[tex] \textsf{Volume}_{\textsf{pyramid}} = \dfrac{1}{3} \times \textsf{Area of base} \times \textsf{height} \\\\ = \dfrac{1}{3} \times (3a \times b) \times 2c \\\\ = 2abc [/tex]
Now, simplify both expressions:
[tex] \textsf{Volume}_{\textsf{prism}} = 2abc [/tex]
[tex] \textsf{Volume}_{\textsf{pyramid}} = 2abc [/tex]
Both expressions simplify the same result, [tex]2abc[/tex].
Therefore, the volume of the prism is equal to the volume of the pyramid.
[tex] \textsf{Volume}_{\textsf{prism}} = \textsf{Volume}_{\textsf{pyramid}} [/tex]
