Answer to Question #335266 in Calculus for gel

Question

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.

Answer 1

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.

$V_{slice}=\pi r^2h=\pi (5)^2h=25\pi \triangle x ft^3$

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

$D_{slice}=9-x$

$W=F_{slice}D_{slice}=(1560\pi \triangle x)(9-x)=1560\pi \int_0^6(9-x)dx=1560\pi (9x-\frac{x^2}{2})|_0^6=1560\pi(36)=56160\pi$