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.
Answer & explanation
Correct answer: option 1
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