# Science:Math Exam Resources/Courses/MATH101/April 2008/Question 06

MATH101 April 2008
Other MATH101 Exams

### 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:

${\displaystyle A(y){\frac {dy}{dt}}=k{\sqrt {y}}}$
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