We have that the formula for the surface area of a cylinder is the following:
[tex]S=2\pi rh+2\pi r^2[/tex]in this case, we have the following:
[tex]\begin{gathered} S=690.8 \\ d=10\Rightarrow r=5 \\ \pi=3.14 \\ \Rightarrow690.8=2(3.14)(5)h+2(3.14)(5)^2 \\ \Rightarrow690.8=31.4h+157 \\ \Rightarrow31.4h=690.8-157=533.8 \\ \Rightarrow h=\frac{533.8}{31.4}=17 \\ h=17 \end{gathered}[/tex]therefore, the length of the height is 17 inches
