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> The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.4 lb/ft3, find the work required to pump the water out of the outlet. The radius of the hemisphere is 10.
##V =\pi x^2 h##
using the equation of a sphere with a center in $\ (0,10)$
##\ x^2 + (y10)^2 = 100##
##\ x^2 = 20yy^2##
And the volume is:
##V =\pi (20yy^2) \Delta y##
the force would be:
##F =62.4 \pi (20yy^2) \Delta y##
And the distance as the image says is:
##d = (10y)##
Finally the work would be:
##\int_0^{10} 62.4 \pi (20yy^2) (10y)\, dy##
And the answer gives me ## 156000 \pi## but according to my textbook the answer have to be ## 41600\pi##
what I'm doing wrong?
> The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.4 lb/ft3, find the work required to pump the water out of the outlet. The radius of the hemisphere is 10.
##V =\pi x^2 h##
using the equation of a sphere with a center in $\ (0,10)$
##\ x^2 + (y10)^2 = 100##
##\ x^2 = 20yy^2##
And the volume is:
##V =\pi (20yy^2) \Delta y##
the force would be:
##F =62.4 \pi (20yy^2) \Delta y##
And the distance as the image says is:
##d = (10y)##
Finally the work would be:
##\int_0^{10} 62.4 \pi (20yy^2) (10y)\, dy##
And the answer gives me ## 156000 \pi## but according to my textbook the answer have to be ## 41600\pi##
what I'm doing wrong?
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