Similar cylinders have proportional dimensions. Find
[tex] k=\dfrac{H}{h} =\dfrac{5}{3} [/tex].
The ratio between surface area is
[tex] \dfrac{SA_{large}}{SA_{small}}=k^2 [/tex].
If large cylinder has surface area=236 sq. cm, then
[tex] \dfrac{236}{SA_{small}}=(\dfrac{5}{3})^2=\dfrac{25}{9},\\ SA_{small}=\dfrac{236\cdot 9}{25} =84.96\approx 85.0 [/tex] sq. cm.
Answer: [tex] SA_{small} =85 [/tex] sq. cm.
