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to design the interior surface of a huge stainless-steel tank, you revolve the curve y=x^2 on the interval 0x4 about the y-axis. the container, with dimensions in meter, is to be filled with sea water, which weighs 10,000 N/m3 . how much work will it take to empty the tank by pumping the water to the tank's top

Respuesta :

jolis1796

Answer:

W = 21.44*10⁶J

Step-by-step explanation:

Given

y = x²    (0 < x < 4)

γ = 10000 N/m³

W = ?

If we apply

y = 4² = 16 = h

y =  x²  ⇒  x = √y

then

V = π*(√y)²*dy = π*y*dy

W = (γ*V) *(16-y) = γ*π*y*dy*(16-y)

⇒  W = γ*π*∫y*(16-y)dy = γ*π*(8y²-(y³/3))

finally we obtain  (0 < y < 16)

W = γ*π*(8y²-(y³/3)) = 10000*π*(8*16²-(16³/3)) = 21.44*10⁶J