Let me draw the situation here below:
Ok, so:
If both cylinders are similar, that means that there's a relation between each other.
Now, the surface area of a cylinder can be found using the next equation:
Surface area = 2πr² + 2πrh.
Where r is the radius, and h is the height.
Notice that we have the surface area for the big cylinder, so, first, we're going to find its radius like this:
236 = 2πr² + 2πr(5)
236 = 2πr² + 10πr
2πr² + 10πr - 236 = 0. Here we have a quadratic equation!
If we solve this quadratic equation, we obtain that r = 4,11896 approximately.
Now, we have to establish a relation between two cylinders.
We have a relation because two figures are similar. So,
5/4.11896 = 3/r
Finding r, we obtain that r (radius of the small cylinder) is r = 2,471376 approximately.
And finally, we calculate the surface area:
Surface area = 2πr² + 2πrh.
SA = 2π(2,471376)² + 2π(2,471376)(3)
Therefore, SA = 84,96. Rounded to the nearest tenth: SA = 85cm²