z=√(5-x^2-y^2) 與 x^2+y^2=4z,聯(lián)立解,消去z,
得 x^2+y^2=4,即交線在xOy平面上的投影.
V =∫∫∫ dv =∫dt∫rdr∫dz
= π∫r[√(5-r^2)-r^2/4]dr
= -π∫√(5-r^2)d(5-r^2) - π∫r^3/4]dr
= π(2/3)[(5-r^2)^(3/2)] - π[r^4/16]
=(2π/3)(5√5-1)-π = 5π(2√5-1)/3.