x^2+y^2=a^2,y^2+z^2=a^2三重积分算体积

x^2+y^2=a^2,y^2+z^2=a^2所围体积,考虑对称性,每个卦限体积相等,只要还求出第一卦限体积再乘以8即可,
积分区域Ω,在ZOY平面投影是1/4圆,0≤y≤a,
0≤z≤√（a^2-y^2),
0≤x≤√（a^2-y^2),即下限为x=0的平面（YOZ平面）,上限为√（a^2-y^2)的柱面,
V=8∫[0,a]dy∫[0,√（a^2-y^2)]dz∫[0,√（a^2-y^2]dx
=8∫[0,a]dy∫[0,√（a^2-y^2)]（√（a^2-y^2）dz
=8∫[0,a] （a^2-y^2)dy
=8(a^2y-y^3/3) [0,a]
=16a^3/3.