Question

Two metallic right circular cones having their height 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere.

What would be the diameter of the resultant sphere?

Answer 1

Let the cones be Cone 1 and Cone 2

Volume of Cone 1 = 1/3 * pi * (2.1)^2 * 4.1 cc
Volume of Cone 2 = 1/3 * pi * (2.1)^2 * 4.3 cc

Total volume of metal after melting both cones = 1/3 * pi * (2.1)^2 * 8.4 cc

Let the Radius of the sphere be - R.
Hence volume of the sphere would be - 4/3 * pi * (R)^3 = 1/3 * pi * (2.1)^2 * 8.4
Solving for R we get -> R ^3 = (2.1)^3
Hence R = 2.1 cm
Therefore the Diameter of the sphere would be 2 * R = 4.2 cm