UPSC CDS 1 2022 Math Paper

Given:
Inner diameter =14cm
Water flows rate =154 litres per minute
Concept used:
Volume of a cylinder =πr2h
Here, r= radius
h= height or length
Calculation:
The Volume of water that flows in one hour =(154×60) liters. [ ∵1 hour =60mins ]
Volume in cm3=(154×60×1000)cm3[∵1 litre =1000cm3]
Inner radius of the pipe =14∕2=7cm.
Let the length of column of water that flows in 1 hour be Hcm. According to the question,
πr2H=(154×60×1000)
⇒(22∕7)×72×H=(154×60×1000)
⇒22×7×H=(154×60×1000)
⇒154H=(154×60×1000)
⇒H=60000cm‌ or ‌0.6km
∴ The speed of water in km∕hr is 0.6