We know
[tex]\boxed{\sf \star TSA_{(Cylinder)}=2\pi r(h+r)}[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=2\times \dfrac{22}{7}\times 4(8+4)[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{176}{7}(12)[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=\dfrac{2112}{7}[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cylinder)}=301.7cm^2[/tex]
Now
- New Radius=2(4)=8cm
- New Height=2(8)=16cm
[tex]\\ \sf\longmapsto TSA_{(New\:Cylinder)}=2\times \dfrac{22}{7}\times 8(16+8)[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{352}{7}(24)[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cylinder)}=\dfrac{8448}{7}[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cylinder)}=1204.7cm^2[/tex]
So
[tex]\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{1204.7}{301.7}[/tex]
[tex]\\ \sf\longmapsto \dfrac{TSA_{(New\:Cylinder)}}{TSA_{(Old\:Cylinder)}}=\dfrac{4}{1}[/tex]
[tex]\\ \sf\longmapsto\underline{\boxed{\bf{ {TSA_{(New\:Cylinder)}}:{TSA_{(Old\:Cylinder)}}=4:1}}}[/tex]
Hence our correct option is Option C
