I attract a photo drawing the round laying on the x-axis.
You are watching: Work required to pump water out of a spherical tank
(get a generic cross-sectional slice)
$V_slice = π·r^2·h$
$V_slice = π·r^2·dy$
So, now I have to uncover out what "r" is."r" is the same as the secluded "x" that the equation of a circle.So,
$x^2 + y^2 = 9$
$x = +/-\sqrt9 - y^2$
$V_slice = π·(9 - y^2)·dy$
and for force:
$F_slice = (62.5)·π·(9 - y^2)$
And no displacement, which i think I have wrong.
$displacement = (7 - y)$
Therefore we only combine where over there is water, so limits of integration would selection from 0 to 6.
So altogether:$W = \displaystyle\int_0^6 (62.5)·π·(9-y^2)·(7 - y)dy$
asked might 6 "17 at 16:07
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