Given,
Diameter of the hemisphere = 14 cm
So, the radius of the hemisphere = 7 cm
Total height of the vessel = 13 cm = h + r
Now,
Inner surface area of the vessel = 2 π r (h + r)
= 2 (22/7)(7) (13)
= 572 cm2
Therefore, the inner surface area of the vessel is 572 cm2.