Need calculus help with Work: finding work of rate of change in circular cone

Calculus
Tutor: None Selected Time limit: 1 Day

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?

Dec 7th, 2015

Thank you for the opportunity to help you with your question!

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.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 7th, 2015

Thank you so much!!

Dec 7th, 2015

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