Two cilinders (C) are similiar if they ratio (R) and heights (H) diameters are proportional.
The ratio of the radii is 3:5
r/R=3/5
R=5/3*r
Since they are similiar, h/H=r/R=3/5
H=5/3h
Area of C1 = 54Pi
[tex]\begin{gathered} A_{C1}=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2 \\ 54\cdot\pi=2\cdot\pi\cdot r\cdot h+2\cdot\pi\cdot r^2 \\ \end{gathered}[/tex]Area of C2 = ?
[tex]\begin{gathered} A_{C2}=2\cdot\pi\cdot R\cdot H+2\cdot\pi\cdot R^2 \\ A_{C2}=2\cdot\pi\cdot(\frac{5r}{3})\cdot(\frac{5h}{3})+2\cdot\pi\cdot(\frac{5r}{3})^2 \\ A_{C2}=2\cdot\pi\cdot(\frac{25}{9})r\cdot h+2\cdot\pi\cdot\frac{25}{9}r^2 \\ A_{C2}=\frac{25}{9}\cdot\lbrack2\cdot\pi\cdot r\cdot h+5\cdot\pi\cdot r^2\rbrack \\ A_{C2}=\frac{25}{9}\cdot54\cdot\pi \\ A_{C2}=150\pi \end{gathered}[/tex]
