所求旋转体的体积=2∫{π[5+√(16-x²)]²-π[5-√(16-x²)]²}dx(自己作图分析)
=40π∫√(16-x²)dx
=40π∫4cosθ*4cosθdθ(令x=4sinθ)
=320π∫[1+cos(2θ)]dθ(应用余弦倍角公式)
=320π*(π/2)
=160π².