Science:Math Exam Resources/Courses/MATH101/April 2018/Question 07 (i)/Solution 1

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Slicing horizontally the reservoir, we get cylindrical pancakes with its height . Since the equation for the circle is , the piece of the circle which lies to the right of the -axis can be parametrized by . Therefore, the pancake at the height from has its radius , and the volume of the pancake at the height is

Since the range of the height is from to , we finally get the volume formula for the reservoir as

Answer: