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UPSC Civil Service Exam Questions - Engineering

Q1:

A cylindrical vessel with a constant plane area of 1 m2 is rotated about its vertical axis such that the liquid inside the vessel is about to spill. If the height of the vessel is 2 m and the height of the paraboloid at 1 m, then the volume (in m3) of the liquid in the vessel will be

A 2

B 1.5

C 1.0

D 0.5

ANS:B - 1.5

Vol(water) = Vol(cylinder) - Vol(paraboloid).
= πr^2h(cyl.) - [πr^2 h(par.) /2].

Since πr^2 = plane area of either Cylinder or Paraboloid = 1 m^2 ; h(cyl.) = 2m ; h(par,) = 1m.

Vol(water) = (1x2) - [(1x1)/2].
= 1.5 m^3.