Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
When balls are melted and recast, the volume of material is kept (here minus the 25% lost). The volume of a sphere is \(\frac{4}{3}\pi r^3\), so the common factor \(\frac{4}{3}\pi\) cancels and only the cubes of the radii need to be compared.
Cubes of the radii: \(2^3+4^3+6^3=8+64+216=288\)
75% of the material is left: \(\displaystyle\frac{3}{4}\times288=216\)
\(r^3=216\), so \(r=6\) cm