UPSC CDS 2 2021 Math Paper

Given, internal radius of hemispherical bowl, r1=18cm
Internal radius of cylindrical bottle, r2=3cm
and internal height of cylindrical bottle, h=4cm
Let n number of bottles are used to empty the bowl.
The bowl will be completely empty, when Volume of n number of cylindrical bottles
= Volume of hemispherical bowl.
⇒‌n×V‌one bottle ‌=V‌bowl ‌
⇒‌n×πr22h=‌

2

3

πr13
⇒‌n×(3)2(4)=‌

2

3

×(18)3
⇒‌n×9×4=‌

2

3

×18×18×18
⇒‌n=‌

2×6×18×18

9×4

‌‌=6×18=108
Hence, 108 number of bottles are used to empty the bowl.