The volume outside the pyramid but inside the prism is 250 cubic centimeters.
Step-by-step explanation:
Step 1:
First, we determine the volumes of the rectangular prism and the pyramid.
The volume of a rectangular prism is calculated by multiplying its length, its width, and its height.
The length and width are both 5 cm while the height is 12 cm.
The volume of the rectangular prism [tex]= (5)(5)(12) = 300[/tex].
The volume of the prism is 300 cubic centimeters.
Step 2:
The volume of a square pyramid is given by [tex]V = a^{2} \frac{h}{3}[/tex], where a is side length and h is the height of the pyramid.
The height of the pyramid is half of the prism, so [tex]h = 6[/tex] cm and [tex]a=5[/tex] cm.
The volume of the pyramid [tex]= 5^{2} (\frac{6}{3} ) = 50.[/tex]
The volume of the pyramid is 50 cubic centimeters.
Step 3:
The volume outside the pyramid but inside the prism [tex]=300 - 50 = 250.[/tex]
The volume is 250 cubic centimeters.
