Science:Math Exam Resources/Courses/MATH101/April 2009/Question 07 (c)
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Question 07 (c) 

An open metal tank has two ends which are isosceles triangles with vertex at the bottom, two sides which are rectangular, and an open top. The tank is 1 metre wide, 2 metres deep, 10 metres long and full of water (density = 1000 kg/m^{3}).

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The rectangular side may seem like a trivial calculation but recall that the width of the rectangle is the same as one of the sides of the triangle and so the length of this side will relate to the triangle in some way. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Hydrostatic Force was not covered in the 2012 offering of this course. Time might better be spent solving other problems given how soon the exam is coming.
Recall that the variable z indicates the distance along the hypotenuse. For a given z we can get the vertical length of the corresponding right triangle, y, as Therefore we have that which we can substitute into our hydrostatic force to get, Now z starts at the bottom of the rectangle (which we will define as z=0) and ends at the full length of the triangular side. We can use Pythagorean theorem to get that the full length of that side is . Therefore we have that the hydrostatic force is, Since we are asked to set up the integral but not evaluate it, we are now done. 