Answer:
The volume of the solid is
[tex]V=\frac{1,960}{3} \pi\ in^3[/tex]
Step-by-step explanation:
step 1
Find the volume of the cylinder
The volume of the cylinder is given by the formula
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=14/2=7\ in[/tex] ---> the radius is half the diameter
[tex]h=20\ in[/tex]
substitute the values
[tex]V=\pi (7)^{2} (20)=980\pi\ in^3[/tex]
step 2
Find the volume of the two congruent hollow cones
The volume of the two cones is given by the formula
[tex]V=2[\frac{1}{3} \pi r^{2}h][/tex]
we have
[tex]r=7\ in[/tex] ---> is the same that the radius of cylinder
[tex]h=10\ in[/tex] ----> is half that the height of cylinder
substitute
[tex]V=2[\frac{1}{3} \pi (7)^{2}(10)][/tex]
[tex]V=\frac{980}{3} \pi\ in^3[/tex]
step 3
To find out the volume of the solid subtract the volume of the two cones from the volume of the cylinder
[tex]V=980\pi-\frac{980}{3} \pi=\frac{1,960}{3} \pi\ in^3[/tex]
