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.
Answer & explanation
Correct answer: option 3
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