A solid metallic hemisphere of radius 6 cm is melted and given the shape of a right circular cone of base radius 4 cm. Determine the height of the cone.

27 cm

Radius of hemisphere = 6 cm

Radius of cone = 4 cm

We know that,

Volume of the hemisphere = 2/3πr³

Volume of the cone = 1/3hπr²

Now let height of the cone = h

2/3πR³ = 1/3hπr²

4R³ = hr²

h = 2R³/ r²

h = (2 × 216)/ 16 = 27 cm