Answer:
[tex]1,233\frac{1}{3}\ in^3[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The volume of the figure is equal to the volume of the cube plus the volume of the square pyramid
Find the volume of the cube
[tex]V=b^3[/tex]
where
b is the length side of the cube
we have
[tex]b=10\ in[/tex]
[tex]V=10^3=1,000\ in^3[/tex]
Find the volume of the square pyramid
[tex]V=\frac{1}{3}b^{2}h[/tex]
where
b is the length side of the square base
h is the height of the pyramid
we have
[tex]b=10\ in[/tex]
[tex]h=17-10=7\ in[/tex]
substitute
[tex]V=\frac{1}{3}(10)^{2}(7)[/tex]
[tex]V=\frac{700}{3}\ in^3[/tex]
Find the volume of the complete figure
Adds the volumes
[tex]V=1,000+\frac{700}{3}=\frac{3,700}{3}\ in^3[/tex]
convert to mixed number
[tex]\frac{3,700}{3}\ in^3=\frac{3,699}{3}+\frac{1}{3}=1,233\frac{1}{3}\ in^3[/tex]
