GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

Question : 62 of 65

Marks: +1, -0

Consider the hemi-spherical tank of radius

13 {m}

as shown in the figure (not drawn to scale). What is the volume of water in

({m}^{3})

when the depth of water at the centre of the tank is

6 {m}

Solution:

Volume generated by the Y axis revolution equation of circle

⇒(x+0)^{2}+(y-13)^{2}=13^{2}

Volume

=π ∫↙{y_{1}}↖{y_2} x^{2} d y

=π ∫↙{0}↖{6}(169-(y-13)^{2}) d y

=396 π

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