UPSC CDS 2 2021 Math Paper

We are given the dimensions as
Cone : r1=x and h1=2x
Hemisphere : r2=x
Cylinder : r3=x and h2=3xWhen the solid is placed into the cylinder then the water equal to the volume of solid will be emptied.
Hence, water left in the cylinder
= Volume of cylinder - Volume of solid
=πr32h2−‌

4

3

πx3
[ ∵ obtained‌in‌question(46)]
‌‌=π⋅x2⋅(3x)−‌

4

3

‌‌=3πx3−‌

4

3

πx3
‌‌=πx3(3−‌

4

3

)=π⋅x3⋅‌

5

3

=‌

5π

3

x3
‌‌=‌

5×3.14

3

x3=‌

15.7

3

x3=5.24x3
Hence, the approximate volume of water left in the cylinder is 524x3.