It can be observed that radius (r) of the cylindrical part and the hemispherical part is the same (i.e., 7 cm).
Height of hemispherical part = Radius = 7 cm
Height of cylindrical part (h) = 13 −7 = 6 cm
Inner surface area of the vessel = CSA of cylindrical part + CSA of hemispherical part
= 2 πrh + 2π r2
Inner surface area of vessel
= 2 x 22/7 x 7 x 6 +2 x 22/7 x 7
= 44(6+7)
= 44 x 13
= 572 cm2