Answer:
339.12 cubic millimeters
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 two hemispheres (one sphere) plus the volume of the cylinder
so
step 1
Find the volume of the cylinder
The volume is given by
[tex]V=Bh[/tex]
where
B is the area of the base of cylinder
h is the height of cylinder
we have
[tex]B=\pi r^{2}[/tex]
we have
[tex]h=8\ mm[/tex]
[tex]r=6/2=3\ mm[/tex] ----> the radius is half the diameter
[tex]B=(3.14)(3)^{2}[/tex]
[tex]B=28.26\ mm^2[/tex]
substitute
[tex]V=(28.26)(8)=226.08\ mm^3[/tex]
step 2
Find the volume of the sphere
The volume is given by
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=6/2=3\ mm[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}(3.14)(3)^{3}=113.04\ mm^3[/tex]
step 3
Adds the volumes
[tex]226.08+113.04=339.12\ mm^3[/tex]
