Answer:
The volume of the pyramid is one third the volume of the rectangular prism
or
The volume of the prism is three times the volume of the pyramid
Step-by-step explanation:
step 1
Find the volume of the rectangular prism
The volume is equal to
![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
where
B is the area of the base
h is the height of the prism
Find the area of the base B
![B=5^{2}=25\ in^{2}](https://tex.z-dn.net/?f=B%3D5%5E%7B2%7D%3D25%5C%20in%5E%7B2%7D)
substitute
![Vprism=25h\ in^{3}](https://tex.z-dn.net/?f=Vprism%3D25h%5C%20in%5E%7B3%7D)
step 2
Find the volume of the square pyramid
The volume is equal to
![V=(1/3)Bh](https://tex.z-dn.net/?f=V%3D%281%2F3%29Bh)
where
B is the area of the base
h is the height of the pyramid
Find the area of the base B
![B=5^{2}=25\ in^{2}](https://tex.z-dn.net/?f=B%3D5%5E%7B2%7D%3D25%5C%20in%5E%7B2%7D)
substitute
![Vpyramid=(1/3)25h\ in^{3}](https://tex.z-dn.net/?f=Vpyramid%3D%281%2F3%2925h%5C%20in%5E%7B3%7D)
Remember that
![Vprism=25h\ in^{3}](https://tex.z-dn.net/?f=Vprism%3D25h%5C%20in%5E%7B3%7D)
substitute
![Vpyramid=(1/3)Vprism](https://tex.z-dn.net/?f=Vpyramid%3D%281%2F3%29Vprism)
The volume of the pyramid is one third the volume of the rectangular prism
or
![Vprism=3Vpyramid](https://tex.z-dn.net/?f=Vprism%3D3Vpyramid)
The volume of the prism is three times the volume of the pyramid