Answer:
[tex]h=17\ in[/tex]
Step-by-step explanation:
we know that
The total surface area of a cylinder is equal to
[tex]SA=2\pi r^{2}+2\pi rh[/tex]
where
r is the radius of the base of cylinder
h is the height of cylinder
we have
[tex]SA=690.8\ in^2[/tex]
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi=3.14[/tex]
substitute the given values and solve for h
[tex]690.8=2(3.14)(5^{2})+2(3.14)(5)h[/tex]
[tex]690.8=157+31.4h[/tex]
Solve for h
[tex]31.4h=690.8-157[/tex]
[tex]31.4h=533.8[/tex]
[tex]h=17\ in[/tex]
