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

Question

Mathematics

Grumpy

8 September, 02:30

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

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Sidney White · Answer 1

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