64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 : 1
When solids are melted and recast, the volume of metal stays the same. So the volume of the big sphere equals the total volume of the 64 small ones.
\(\displaystyle \frac{4}{3}\pi R^3=64\times\frac{4}{3}\pi r^3\)
The common factor \(\frac{4}{3}\pi\) cancels: \(R^3=64r^3\)
Taking cube roots (\(64=4^3\)): \(R=4r\), so \(R:r=4:1\)