Two similar cylinders have proportional dimensions:
d is the diameter of the second cylinder base, then r=d/2=3 cm.
The surface area of the smaller cylinder consists of the area of two bases and area of the lateral face:
Since r=3 cm and h=9 cm, you have
To first tackle this question, use similarity ratio, where the missing diameter is d. 10/15 = d/9 which can be simplified into d = 6. Then use the surface formula
2πrh + 2πr². Then, since the radius is 0.5d, the radius or r is 3. Then, plus in values and simplify to get 226.19cm².