Science:Math Exam Resources/Courses/MATH103/April 2011/Question 04 (a)
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Question 04 (a) 

Consider the function for 0 ≤ x ≤ 1. Find the volume of the horn when rotating around a horizontal axis at . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Draw a picture. 
Hint 2 

Make slices (orthogonal to the axis of rotation) and integrate. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Following the hints, we slice this "horn" into circular pieces. The volume of each slice is equal to where is the radius of the circle and is its thickness. Hence, in the limit 