Answer:
[tex]W=17085KJ[/tex]
Explanation:
From the question we are told that:
Height [tex]H=16m[/tex]
Radius [tex]R=3[/tex]
Height of water [tex]H_w=9m[/tex]
Gravity [tex]g=9.8m/s[/tex]
Density of water [tex]\rho=1000kg/m^3[/tex]
Generally the equation for Volume of water is mathematically given by
 [tex]dv=\pi*r^2dy[/tex]
 [tex]dv=\frac{\piR^2}{H^2}(H-y)^2dy[/tex]
Where
  y is a random height taken to define dv
Generally the equation for Work done to pump water is mathematically given by
 [tex]dw=(pdv)g (H-y)[/tex]
Substituting dv
 [tex]dw=(p(=\frac{\piR^2}{H^2}(H-y)^2dy))g (H-y)[/tex]
 [tex]dw=\frac{\rho*g*R^2}{H^2}(H-y)^3dy[/tex]
Therefore
 [tex]W=\int dw[/tex]
 [tex]W=\int(\frac{\rho*g*R^2}{H^2}(H-y)^3)dy[/tex]
 [tex]W=\rho*g*R^2}{H^2}\int((H-y)^3)dy)[/tex]
 [tex]W=\frac{1000*9.8*3.142*3^2}{9^2}[((9-y)^3)}^9_0[/tex]
 [tex]W=3420.84*0.25[2401-65536][/tex]
 [tex]W=17084965.5J[/tex]
 [tex]W=17085KJ[/tex]
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