Question #335266

A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.




(a). assuming that the tank is half-filled with water.

1
Expert's answer
2022-05-03T13:52:26-0400

Let Ax be the height of the water, p= 5 ft be the radius of the cylinder tank and d=62.4 lb/ft? be the weight-density of water.

Vslice=πr2h=π(5)2h=25πxft3V_{slice}=\pi r^2h=\pi (5)^2h=25\pi \triangle x ft^3

Fslice=dV=62.425πx=1560πx(lb)F_{slice}=dV=62.4*25\pi \triangle x =1560\pi \triangle x (lb)

Dslice=9xD_{slice}=9-x

W=FsliceDslice=(1560πx)(9x)=1560π06(9x)dx=1560π(9xx22)06=1560π(36)=56160πW=F_{slice}D_{slice}=(1560\pi \triangle x)(9-x)=1560\pi \int_0^6(9-x)dx=1560\pi (9x-\frac{x^2}{2})|_0^6=1560\pi(36)=56160\pi


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