



 
Hi Susan, Cute project! Here is a sketch of the cone shaped top. You have a right triangle with legs of length 17.5" and 30" and hypotenuse of length r inches so Pythagoras theorem says that
or
If you took the material from the cone in the diagram and cut it along one of the seams it will then lie flat in the shape of a sector of a circle as in the diagram below. The circumference of the hula hoop is π × diameter = π × 35 = 109.0 inches which is the length of the arc in the sector above. This is a sector of a circle with radius 34.7 inches or diameter 69.4 inches so the circumference of this circle is π × diameter = π × 69.4 = 218.0 inches. Thus the arc length is half the circumference and hence the sector is a semicircle. Hence if you cut a semicircle of radius 34.7 inches which is about 34 3/4 inches it will form the cone you need. Unfortunately this leaves no material for a seam. If your material is 36 inches wide I would cut a piece like this leaving you an inch and a quarter for seams. If you complete this project send us a photo so we can post it. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 