Radius of cone: $r = \sqrt{l^2 - h^2} = \sqrt{13^2 - 12^2} = \sqrt{169-144} = 5$ cm.
Total height = height of cone + radius of hemisphere = 12 + 5 = 17 cm. → Option A
The hemisphere's radius equals the cone's base radius (r = 5 cm). The hemisphere adds its radius (not diameter) to the cone's height, giving 12 + 5 = 17 cm. A common mistake is adding the diameter (10 cm) instead.