Science:Math Exam Resources/Courses/MATH101/April 2007/Question 05/Statement

Full-Solution Problem. Justify your answers and show all your work. Simplification of answers is not required.

A paper cup has the shape depicted below. All of its horizontal cross sections are circles; the radius of the cup's bottom is 3 cm and the radius of its top is 6 cm. The cup is full of Cona Cola, which has a density of 1000 kg/$m^{3}$. The Cona Cola is drunk through a vertical straw that extends 10 cm above the top of the cup and reaches the bottom of the cup. Express as an explicit definite integral the work performed in drinking all the cola. Do not evaluate this integral. For the acceleration due to gravity, use the value $9.8m/s^{2}$.