UPSC CDS 1 2022 Math Paper

Given:
Radius of the base the cylindrical container =18cm
Radius of metal balls =0.9cm
Water level raised by 3cm
Concept used:
Volume of cylinder =πr2h
Volume of sphere =(4πr3)∕3
Calculation:
Volume of the increased water level =π×182×3
Let n number of metal balls be required
According to the question,
[(4×π×0.93)∕3}×n=π×182×3
⇒n=(324×3×3×103)∕(4×93)[∵0.9=9∕10]
⇒n=(324×103)∕(4×81)
⇒n=(324×103)∕324
⇒n=103‌ or ‌1000
∴ Required number of balls required to raise the water level are 1000