Answer:
The volume of the composite figure is equal to [tex]400\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the composite figure is equal to the area of the rectangular prism plus the volume of the rectangular pyramid
step 1
Find the volume of the rectangular prism
The volume is equal to
[tex]V=LWH[/tex]
we have
[tex]L=12\ in[/tex]
[tex]W=4\ in[/tex]
[tex]H=5\ in[/tex] ----> height of the rectangular prism
substitute
[tex]V=12*4*5=240\ in^{3}[/tex]
step 2
Find the volume of the rectangular pyramid
The volume is equal to
[tex]V=\frac{1}{3}LWh[/tex]
we have
[tex]L=12\ in[/tex]
[tex]W=4\ in[/tex]
[tex]h=10\ in[/tex] ----> height of the rectangular pyramid
substitute
[tex]V=\frac{1}{3}(12)(4)(10)=160\ in^{3}[/tex]
step 3
Adds the volumes
[tex]240\ in^{3}+160\ in^{3}=400\ in^{3}[/tex]
