A tank containing oil is in the shape of a downward-pointing cone with its vertical axis perpendicular to ground level. (See a graph of the tank here.) In this exercise we will assume that the height of the tank is 10 ft , the circular top of the tank has radius 5 ft, and that the oil inside the tank weighs 56 lb per cubic ft.
How much work does it take to pump oil from the tank to an outlet that is 3 ft above the top of the tank if, prior to pumping, there is only a half-tank of oil? Note: "half-tank" means half the volume in the tank.

Question

A tank containing oil is in the shape of a downward-pointing cone with its vertical axis perpendicular to ground level. (See a graph of the tank here.) In this exercise we will assume that the height of the tank is 10 ft , the circular top of the tank has radius 5 ft, and that the oil inside the tank weighs  56 lb per cubic ft. 
How much work  does it take to pump oil from the tank to an outlet that is 3 ft  above the top of the tank if, prior to pumping, there is only a half-tank of oil?   Note: "half-tank" means half the volume in the tank.

anonymous · Answer

Have you started yet?

anonymous · Answer

yes I have I don't know what to do wiht the volume. How to I half it

anonymous · Answer

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anonymous · Answer

Oky I have got a picture of that already

anonymous · Answer

Sorry, site bugged out on me

anonymous · Answer

mass of a slab is thickness (dy)  times area of slab (as a function of y) times density of the oil

anonymous · Answer

i am just confused on how to find the cross sectional area. what does it mean by half too? likw so comfused

anonymous · Answer

force required to lift that slab is mass times g
and the distance to lift it is the distance between the slab and the outlet..

anonymous · Answer

ok..  let's sketch some stuff.... remember we want everything determined in terms of y

anonymous · Answer

right

anonymous · Answer

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