



 
It's easy if you know how to integrate. First, for a picture of half the object, look at our web page: This shape can be used for domes of public buildings, almost like the Saskatchewan Legislative Building, where I say "almost" because they used perpendicular ellipses rather than circles for the dome. For the volume I would I would take the common diameter to be the xaxis  just rotate the first figure clockwise so that one of the circles becomes the equator. I recommend that you find the volume of the right half, then multiply that number by 2 for your final answer. Thus you integrate the area of the square cross section times dx, from x = 0 to x = a. For each x you know the diagonal of the square to be y = 2*sqrt(a^2  x^2). From that you can get the side of the square and then the area of the cross section. Chris  


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