Answer :
Answer:
Explanation:
Let the height of the small cylinder be h
Let the radius of the small cylinder be r
The surface area of the small cylinder is:
[tex]SA_{small}=2\pi r(r+h)[/tex]Simplify the expression by setting SA = 20π
[tex]\begin{gathered} 20\pi=2\pi r(r+h) \\ \\ \frac{20\pi}{2\pi}=r(r+h) \\ \\ 10=r(r+h).........(1) \end{gathered}[/tex]Let the height of the large cylinder be H
Let the radius of the large cylinder be R
The surface area of the large cylinder will be:
[tex]\begin{gathered} SA_{large}=2\pi R(R+H) \\ \\ 90\pi=2\pi R(R+H) \\ \\ \frac{90\pi}{2\pi}=R(R+H) \\ \\ 45=R(R+H).......(2) \end{gathered}[/tex]Divide equation (2) by equation (1)
[tex]\begin{gathered} \frac{45}{10}=\frac{R(R+H)}{r(r+h)} \\ \\ 4.5=\frac{R(R+H)}{r(r+h)} \\ \\ \\ \end{gathered}[/tex]