所求环体的体积

=∫[π(5+√(16-x²))²-π(5-√(16-x²))²]dx

=40π∫√(16-x²)dx

=40π∫4cost*4costdt (令x=4sint)

=320π∫[1+cos(2t)]dt (应用倍角公式)

=320π[t+sin(2t)/2]│

=320π(π/2-0)

=160π²