A reservoir shaped like a right circular cone point down, 20 ft across the top and 8 ft deep, is full of water. How much work does it take to pump the water to a level 6 ft above the top?
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delta V = pi ( radius)^2 ( thickness) = pi [(5/4)y]^2 delta y cubic feet
Force F(y) = 62.4 * pi (25/26)y^2 delta y
Delta W = 62.4 pi (25/16) y^2 ( 8 - y) delta y
W = integral from 0 to 6 [ 62.4 pi (25/16) y^2 (8-y) dy
= 97.5 pi [ integral from 0 to 6 ( y^2( 8-y)dy
= 97.5 pi (252) = 24570 pi = 77188. 93 ft - lb.
Thank you so much!!
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