The number of iron balls, each 1 cm in radius, that can be made from an iron sphere of diameter 12 cm is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 216
When the sphere is melted and recast, the amount of iron does not change, so the number of balls is the volume of the big sphere divided by the volume of one ball. The big sphere has radius 6 cm.
Volume of the big sphere: \(\frac{4}{3}\pi\times6^{3}\)
Volume of one ball: \(\frac{4}{3}\pi\times1^{3}\)
Number of balls: \(\displaystyle\frac{6^{3}}{1^{3}}=216\), as \(\frac{4}{3}\pi\) cancels