Question

Can you please help me out with a question

Answer 1

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

`\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}`

Area of C2 = ?

`\begin{gathered} A_(C2)=2\cdot\pi\cdot R\cdot H+2\cdot\pi\cdot R^2 \\ A_(C2)=2\cdot\pi\cdot((5r)/(3))\cdot((5h)/(3))+2\cdot\pi\cdot((5r)/(3))^2 \\ A_(C2)=2\cdot\pi\cdot((25)/(9))r\cdot h+2\cdot\pi\cdot(25)/(9)r^2 \\ A_(C2)=(25)/(9)\cdot\lbrack2\cdot\pi\cdot r\cdot h+5\cdot\pi\cdot r^2\rbrack \\ A_(C2)=(25)/(9)\cdot54\cdot\pi \\ A_(C2)=150\pi \end{gathered}`