A metallic cone of radius 12 cm and height 36 cm is melted and made into spheres of radius 3 cm each. How many spheres are there?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 48.
Volume of the cone = (1/3) × π × r² × h = (1/3) × π × 12² × 36 = (1/3) × π × 144 × 36 = π × 1728 cm³
Volume of one sphere = (4/3) × π × r³ = (4/3) × π × 3³ = (4/3) × π × 27 = π × 36 cm³
Number of spheres = Volume of cone / Volume of one sphere = (π × 1728)/(π × 36) = 1728/36 = 48 spheres