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.