Given:-$\text{Height of Cone}(h)=12\ \text{cm}$$\text{Slant height of Cone}(l)=13\ \text{cm}$we know that,$l^2 = h^2 + r^2$$(13)^2 = (12)^2 + r^2$$169 = 144 + r^2$$r^2 = 169 - 144$$r^2 = 25$$\therefore r = \sqrt{25} = 5\ \text{cm}$The Cone is surmounted on a hemisphere radius of the hemisphere is equal to the radius of the cone.Height of the Cone (h) = 12 cmRadius of the hemisphere (r) = 5 cm∴ The Total height of the Solid = 12 cm + 5 cm= 17 cm