Solution:

Given radius of the hemisphere, r = 8 cm

Volume of the hemisphere, V = (2/3)r³

= (2/3)×8³

= (1024/3) cm³

Radius of cone, R = 6 cm

Since hemisphere is melted and recasted into a cone, the volume remains the same.

Volume of the cone, (1/3)R²h = (1024/3)

(1/3)×6² ×h = (1024/3)

36h = 1024

h = 1024/36

= 28.44 cm

Hence the height of the cone is 28.44 cm.