 
Summary: Math 1550 Fall 2005
Section 31 P. Achar
Extra Credit Solutions
Due: December 6, 2005
1. (3 points) A 4sphere is made by stacking up crosssections that are 3spheres. Following the pattern
from 2 and 3spheres, set up an integral for the 4volume of a 4sphere of radius r.
Solution: Imagine a 4sphere of radius r centered at the origin in 4dimensional space. If you take a
"slice" perpendicular to the xaxis, you get a 3sphere. Moreover, the radius of that slice is
r2  x2.
The possible values of x are from r to r, so to compute the 4volume by crosssections, we set up the
integral:
r
r
3volume of the
crosssection
dx =
r
r
3volume of a 3sphere
