Answer:
Part 1) The shapes that make up the figure are two hemispheres and a cylinder
Part 2) see the explanation
Part 3) see the explanation
Part 4) [tex]V=34\frac{2}{3}\pi\ mm^3[/tex]
Step-by-step explanation:
Part 1) Define the shapes that make up the figure.
we know that
The shapes that make up the figure are two hemispheres and a horizontal cylinder
Part 2) Identify the volume formula(s) that will be be used for each shape in number 1.
we know that
The volume of a hemisphere is equal to
[tex]V=\frac{2}{3}\pi r^{3}[/tex]
where
r is the radius of the hemisphere
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
where
r is the radius of the base of cylinder
h is the height or length of the cylinder
Part 3) Find the volume for each individual shape.
step 1
Find the volume of a hemisphere
[tex]V=\frac{2}{3}\pi r^{3}[/tex]
we have
[tex]r=2\ mm[/tex]
substitute
[tex]V=\frac{2}{3}\pi (2)^{3}[/tex]
[tex]V=\frac{16}{3}\pi\ mm^{3}[/tex]
step 2
Find the volume of the horizontal cylinder
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]h=10-2-2=6\ mm[/tex]
substitute
[tex]V=\pi (2)^{2}(6)[/tex]
[tex]V=24\pi\ mm^3[/tex]
Part 4) Find the composite volume of the original figure
The volume of the composite figure is equal to the volume of two hemisphere plus the volume of the cylinder
so
[tex]V=2(\frac{16}{3}\pi)+24\pi\\\\V=\frac{32}{3}\pi+24\pi[/tex]
[tex]V=\frac{104}{3}\pi\ mm^3[/tex]
Convert to mixed number
[tex]\frac{104}{3}\pi\ mm^3=\frac{102}{3}\pi+\frac{2}{3}\pi=34\frac{2}{3}\pi\ mm^3[/tex]
