MATH101 April 2008

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q1 (d)  •  Q1 (e)  •  Q1 (f)  •  Q1 (g)  •  Q2 (a)  •  Q2 (b)  •  Q2 (c)  •  Q2 (d)  •  Q3 (a)  •  Q3 (b)  •  Q3 (c)  •  Q3 (d)  •  Q4 (a)  •  Q4 (b)  •  Q5 (a)  •  Q5 (b)  •  Q6  •  Q7 (a)  •  Q7 (b)  •  

   Other MATH101 Exams
  •  April 2018  •  April 2017  •  April 2016  •  April 2015  •  April 2014  •  April 2013  •  April 2012  •  April 2011  •  April 2010  •  April 2009  •  April 2008  •  April 2007  •  April 2006  •  April 2005  •  

Question 06

A paper cup has the unusual shape depicted below. All of its horizontal cross sections are squares, with the top of the cup a square of side length 6 cm and the cup has a height of 10 cm. The cup is initially full of Jolting Java, a potent coffee drink. The precious liquid is leaking from a small hole at the bottom of the cup. After 10 minutes, the height of the coffee above the bottom of the cup has decreased from 10 cm to 5 cm. After how many more minutes will the cup be completely empty? Assume the coffeee drains according to Toricelli's Law, which is stated below. Here, y is the height of the top surface of the coffee above the bottom of the cup, A(y) is the area of the horizontal cross-section of the cup at height y above the bottom, and k is a positive constant. (Also, assume that no coffee is drunk or lost to evaporation.)

Toricelli's Law:

Math Exam Resources Courses MATH101 April 2008 Question 6 picture 1.png

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.



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.

  • If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
  • If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.




Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Integration in physics
lightbulb image
Math Learning Centre
  • A space to study math together.
  • Free math graduate and undergraduate TA support.
  • Mon - Fri: 11 am - 5 pm, LSK 301&302.

Private tutor