First, we find the volume of the cylindrical object then we subtract the volume of the cone-shaped hole. Therefore:
-The volume of the cylinder is given by
[tex]V=\pi\cdot r^2\cdot h[/tex]
Where
r = 5 inches
h = 15 inches
So,
[tex]V=\pi\cdot(5)^2\cdot15=(3.14)\cdot25\cdot15=1177.5[/tex]
-The volume of the hole is given by
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]
Where
r = D/2 = 6/2 = 3 inches
h = 9 inches
[tex]V=\frac{\pi\cdot(3)^2\cdot9}{3}=\frac{\pi\cdot9\cdot9}{3}=\frac{\pi\cdot81}{3}=27\pi=27(3.14)=84.78[/tex]
Next, the volume of the cylindrical object is
[tex]V=1177.5-84.78=1092.72[/tex]
Answer: 1092.72 cubic inches
