UPSC CDS 1 2022 Math Paper

Given:
Height of cylindrical tank=1m
Diameter of tank=2m
Radius of spherical droplet =1cm
Formula used:
Calculation:
The volume of the cylinder =π(1)2×1 cubic meter
Since 1 meter =100cm
⇒ The volume of the cylinder =π(100)2×100
The volume of spherical droplet =(4∕3)π×13
⇒ The volume of spherical droplet =4π∕3
Therefore, 4π∕3cm3 volume decreases per second.
Hence,
Time required to empty tank = Volume of cylinder\/water discharge
⇒[π(100)2×100]∕(4π∕3)
⇒75×104sec
⇒75×104∕3600hr‌‌[∵1hr=3600sec]
⇒208.33≈210hr
The tank will be emptied in approximately 210 hour: