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So a cousin has asked me for Calculus help, but my Calculus is rusty. She's in Calculus II (of a 3-semester sequence in the US) and is on Work. I decided to make up a problem for her, but I want to make sure I know what I'm doing.
A cylindrical tank (16 feet high with a radius of 4 feet) is half full of beer that weighs 63 pounds per cubic foot. Find the work requred to pump beer out through a spout in the top of the tank.
[itex]W = {\int_a}^b F(x) dx[/itex]
I just would like to know if I had set up the integral right.
The volume of a disk of beer would be [itex]\pi \cdot 4^2 \Delta\ y[/itex]
The weight of a disk of beer would be [itex]63 \cdot 16\pi \Delta y = 1008\pi \Delta y[/itex]
The distance to move a disk of beer to the top would be [itex]16 - y[/itex]
[itex]W = {\int_0}^8 1008\pi (16 - y) dy[/itex]
Is the integral this? Seems too simple. If so, I can take it from here.
Thanks in advance.
Homework Statement
A cylindrical tank (16 feet high with a radius of 4 feet) is half full of beer that weighs 63 pounds per cubic foot. Find the work requred to pump beer out through a spout in the top of the tank.
Homework Equations
[itex]W = {\int_a}^b F(x) dx[/itex]
The Attempt at a Solution
I just would like to know if I had set up the integral right.
The volume of a disk of beer would be [itex]\pi \cdot 4^2 \Delta\ y[/itex]
The weight of a disk of beer would be [itex]63 \cdot 16\pi \Delta y = 1008\pi \Delta y[/itex]
The distance to move a disk of beer to the top would be [itex]16 - y[/itex]
[itex]W = {\int_0}^8 1008\pi (16 - y) dy[/itex]
Is the integral this? Seems too simple. If so, I can take it from here.
Thanks in advance.