Here is what i understand from the problem...
We have the middle section which is a cylinder and has a radius 8 cm.
So surface area for the cylindrical part of the ball will be only the curved surface = 2∏ r H, where H is the length of the cylinder and r the radius.
we know r =8cm
Now the entire length of the ball is 25 cm. The two ends have hemispheres with radius 8cm. So the cylindrical part has length = 25-8-8 = 9 cm. So H = 9cm
So surface area = 452.39 sq cm..............(1)
Now the two ends of the ball are hemispheres with radius 8cm. surface area of the 2 hemispheres for the ball is the curved portion of the 2 hemispheres and combined will be 4∏r2 = 804.25 sq cm.....................(2)
Now we add the 2 areas and get the surface area of the ball = 1256.64 sq cm
That is your answer for part (a)
Now for the part (b) to get the cost we multiply the surface area by the cost for unit area = 1256.64*0.11 = 138.23 $