January 31, 2006 Lecturer: Dr Martin Kurth Hilary Term 2006 Course 1E1 2005-2006 (JF Engineers & JF MSISS & JF MEMS) Problem Sheet 3 Due: in the Tutorials February 10 / February 13 Revolutions never occur in mathematics. from: Michael Crowe Historia Mathematica 1. Calculate the volume of a column of height 4, with a radius of 1 at the top and a radius of 2 at the bottom (ie the volume of a part of a cone). (4 points) 2. Calculate the volume of the solid generated by revolving the area bounded √ by the graphs of y = x + 4 and y = 18x about the x-axis. (6 points) 3. Your local baker sells you a doughnut of volume 60cm3 . As a proper engineer you measure the doughnut before you eat it, and find that its inner radius is 2cm while its outer radius is 4cm. Have you been cheated by your baker? (*) Questions 1 and 2 should be answered by all students, you will get points for them. Question 3 is more challenging and meant as an exercise for the more mathematically interested students.