Given: Two solid hemispheres of radius r joined at a single point.For a single solid hemisphere of radius r:Curved Surface Area (CSA) = $2\pi r^{2}$Area of the flat circular base = $\pi r^{2}$Total Surface Area (TSA) of one solid hemisphere = $2\pi r^{2}$ + $\pi r^{2}$ = $3\pi r^{2}$Since the two hemispheres are joined at a single point, no part of their surface area is hidden or lost.Total surface area of the object = TSA of $1^{st}$ hemisphere + TSA of $2^{nd}$ hemisphere= $3\pi r^{2}$ + $3\pi r^{2}$ = $6\pi r^{2}$Therefore, the total surface area of the object is $6\pi r^{2}$.