Two metallic right circular cones having same base radius 2.1 cm and heights 4.1 cm and 4.3 cm respectively, have been melted together and given  a shape of a sphere. Find the radius of the sphere.

2.1 cm

Total volume of both the cones are = \(\frac{1}{3}\) × π ×2.1² × 4.1+ \(\frac{1}{3}\) × π ×2.1² × 4.3

= \(\frac{1}{3}\) × π ×2.1² ( 4.1 + 4.3 )

Volume of sphere = \(\frac{4}{3}\) × π  × r³

\(\frac{4}{3}\) × π  × r³ = \(\frac{1}{3}\) × π ×2.1² ( 8.4 ) 

4  × r³ = 2.1² ( 8.4 )

r = 2.1

The correct answer is option (1) : 2.1 cm