Line 1 slope is -1
Line 2 slope is 4/5
I believe the answer is 54%.
Hope this helps!
Parameterize the lateral face
![T_1](https://tex.z-dn.net/?f=T_1)
of the cylinder by
![\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v](https://tex.z-dn.net/?f=%5Cmathbf%20r_1%28u%2Cv%29%3D%28x%28u%2Cv%29%2Cy%28u%2Cv%29%2Cz%28u%2Cv%29%29%3D%282%5Ccos%20u%2C2%5Csin%20u%2Cv)
where
![0\le u\le2\pi](https://tex.z-dn.net/?f=0%5Cle%20u%5Cle2%5Cpi)
and
![0\le v\le3](https://tex.z-dn.net/?f=0%5Cle%20v%5Cle3)
, and parameterize the disks
![T_2,T_3](https://tex.z-dn.net/?f=T_2%2CT_3)
as
![\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)](https://tex.z-dn.net/?f=%5Cmathbf%20r_2%28r%2C%5Ctheta%29%3D%28x%28r%2C%5Ctheta%29%2Cy%28r%2C%5Ctheta%29%2Cz%28r%2C%5Ctheta%29%29%3D%28r%5Ccos%5Ctheta%2Cr%5Csin%5Ctheta%2C0%29)
![\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)](https://tex.z-dn.net/?f=%5Cmathbf%20r_3%28r%2C%5Ctheta%29%3D%28r%5Ccos%5Ctheta%2Cr%5Csin%5Ctheta%2C3%29)
where
![0\le r\le2](https://tex.z-dn.net/?f=0%5Cle%20r%5Cle2)
and
![0\le\theta\le2\pi](https://tex.z-dn.net/?f=0%5Cle%5Ctheta%5Cle2%5Cpi)
.
The integral along the surface of the cylinder (with outward/positive orientation) is then
![\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_S%28x%5E2%2By%5E2%2Bz%5E2%29%5C%2C%5Cmathrm%20dS%3D%5Cleft%5C%7B%5Ciint_%7BT_1%7D%2B%5Ciint_%7BT_2%7D%2B%5Ciint_%7BT_3%7D%5Cright%5C%7D%28x%5E2%2By%5E2%2Bz%5E2%29%5C%2C%5Cmathrm%20dS)
![=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_%7Bu%3D0%7D%5E%7Bu%3D2%5Cpi%7D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D3%7D%28%282%5Ccos%20u%29%5E2%2B%282%5Csin%20u%29%5E2%2Bv%5E2%29%5Cleft%5C%7C%7B%7B%5Cmathbf%20r%7D_1%7D_u%5Ctimes%7B%7B%5Cmathbf%20r%7D_2%7D_v%5Cright%5C%7C%5C%2C%5Cmathrm%20dv%5C%2C%5Cmathrm%20du%2B%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7D%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7D%28%28r%5Ccos%5Ctheta%29%5E2%2B%28r%5Csin%5Ctheta%29%5E2%2B0%5E2%29%5Cleft%5C%7C%7B%7B%5Cmathbf%20r%7D_2%7D_r%5Ctimes%7B%7B%5Cmathbf%20r%7D_2%7D_%5Ctheta%5Cright%5C%7C%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20dr%2B%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7D%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7D%28%28r%5Ccos%5Ctheta%29%5E2%2B%28r%5Csin%5Ctheta%29%5E2%2B3%5E2%29%5Cleft%5C%7C%7B%7B%5Cmathbf%20r%7D_3%7D_r%5Ctimes%7B%7B%5Cmathbf%20r%7D_3%7D_%5Ctheta%5Cright%5C%7C%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20dr)
![=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle2%5Cint_%7Bu%3D0%7D%5E%7Bu%3D2%5Cpi%7D%5Cint_%7Bv%3D0%7D%5E%7Bv%3D3%7D%28v%5E2%2B4%29%5C%2C%5Cmathrm%20dv%5C%2C%5Cmathrm%20du%2B%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7D%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7Dr%5E3%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20dr%2B%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7D%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7Dr%28r%5E2%2B9%29%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20dr)
![=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle4%5Cpi%5Cint_%7Bv%3D0%7D%5E%7Bv%3D3%7D%28v%5E2%2B4%29%5C%2C%5Cmathrm%20dv%2B2%5Cpi%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7Dr%5E3%5C%2C%5Cmathrm%20dr%2B2%5Cpi%5Cint_%7Br%3D0%7D%5E%7Br%3D2%7Dr%28r%5E2%2B9%29%5C%2C%5Cmathrm%20dr)
Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees, so no.