Answer:
[tex]500\ cm[/tex]
Step-by-step explanation:
step 1
Find the volume of hollow cylinder
[tex]V=\pi (r2^{2}-r1^{2})h[/tex]
we have
[tex]r2=8\ cm[/tex]
[tex]r1=6\ cm[/tex]
[tex]h=35\ cm[/tex]
substitute
[tex]V=\pi (8^{2}-6^{2})(35)[/tex]
[tex]V=\pi (28)(35)[/tex]
[tex]V=980\pi\ cm^{3}[/tex]
step 2
we know that
The wire is a solid cylinder with the same volume of the hollow cylinder
so
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=980\pi\ cm^{3}[/tex]
[tex]r=2.8/2=1.4\ cm[/tex] ----> the radius is half the diameter (thickness)
substitute and solve for h
[tex]980\pi=\pi (1.4)^{2}h[/tex]
[tex]980=(1.96)h[/tex]
[tex]h=980/(1.96)=500\ cm[/tex]
