Answer:
[tex]250\ cm^3[/tex]
Step-by-step explanation:
step 1
Find the volume of the prism
The volume of the prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=5\ cm\\W=5\ cm\\H=12\ cm[/tex]
substitute
[tex]V=(5)(5)(12)=300\ cm^3[/tex]
step 2
Find the volume of the pyramid
The volume of the pyramid is
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
[tex]B=5^2=25\ cm^2[/tex]
[tex]h=12/2=6\cm[/tex] ---> half the height of the prism
substitute
[tex]V=\frac{1}{3}(25)(6)=50\ cm^3[/tex]
step 3
we know that
The volume of the space outside the pyramid but inside the prism is equal to subtract the volume of the pyramid from the volume of the cylinder
[tex]300\ cm^3-50\ cm^3=250\ cm^3[/tex]
