The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick, What is the total surface area (in $$cm^2$$) of the vessel?

Internal diameter of hollow hemispherical vessel = 24 cm

Internal radius(r) = 24/2 = 12 cm

External radius(R) = r + thickness of sheet = 12 + 0.5 = 12.5 cm

Surface area of internal vessel = 2$$\pi \times r^2 = 2\pi \times 12^2 = 288\pi$$

Surface area of external vessel = 2$$\pi \times R^2 = 2\pi \times (12.5)^2 = 312.5\pi$$

Surface area of the ring = $$\pi(R^2 - r^2) = \pi(12.5^2 - 12^2) = \pi(156.25 - 144) = 12.25\pi$$

Total surface area = $$288\pi + 312.5\pi + 12.25\pi = 612.75\pi$$