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When they state "solid", you can assume that the entire object is enclosed, unless stated otherwise in a question.
Total Surface Area (SA) in this case is thus as such,
Total SA = Exposed SA for hemisphere + Exposed SA for cylinder
Total SA = 3π(3r)^2 - π(r)^2 + πr(2r) + π(r)^2
Total SA = 29π(r)^2
Total Surface Area (SA) in this case is thus as such,
Total SA = Exposed SA for hemisphere + Exposed SA for cylinder
Total SA = 3π(3r)^2 - π(r)^2 + πr(2r) + π(r)^2
Total SA = 29π(r)^2