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 .
The volume of the prism is 300 cubic centimeters.
Step 2:
The volume of a square pyramid is given by , where a is side length and h is the height of the pyramid.
The height of the pyramid is half of the prism, so cm and cm.
The volume of the pyramid
The volume of the pyramid is 50 cubic centimeters.
Step 3:
The volume outside the pyramid but inside the prism
The volume is 250 cubic centimeters.