The total surface area of a solid hemisphere of radius r equals:

1. The curved surface of a hemisphere equals half the sphere's surface, 2 π r². 2. The flat circular base of the hemisphere has area π r². 3. Total = 2 π r² + π r² = 3 π r². 4. So total surface area of a solid hemisphere = 3 π r². 5. 2 π r² alone misses the circular base; 4 π r² is the full sphere. _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._