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Question: Draining a shaped container from the top, and the amount of Joule it takes to do it.

Question:Draining a shaped container from the top, and the amount of Joule it takes to do it.

The function 110 Maple
integration physics
December 02 2021
1

Hello everybody. Ive got some questions. 

As the title states: Draining a shaped container from the top, and the amount of Joule it takes to do it. That is what the questions are about. 

I did make the first one, and some attempts at the sphere questions b, and c. I left them out because i want to see what you guys come up with. I think ive got the right answers, but we will see if our answers compare. :) 

The Dutch text translated: Calculate in questions a, b, and c the amount of work (joule, J) it takes to drain a tank filled with water from the top with a pump. Each question has a discription of the shape of the tank. Take for gravity g=9.81m/s^2. For water take rho=1000kg/m^3.

a.
A coneshaped tank, the topangle is down, with a height of 2.0meters and a radius of 0.5meters. 

b.
A sphere with a radius of 1.0meters.

c.
The lower half of a sphere with a radius 2.0meters. 

Greetings,

The Function. 

> 

"f(x):=(Pi*(x/(4))^(2)*x)/(3)*9.81"

proc (x) options operator, arrow, function_assign; (1/48)*Pi*x^2*x*9.81 end proc

 (1)
> 

1000*(int(f(x), x = 0 .. 2))

2568.251995

 (2)
> 

``

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